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GIFT  OF 


Dr.tHA^   T^v 


ELEMENTS'        .  - 

OF  '  f4C<,<U<)^ 

L  O  G  I  C. 

IN 


BOOK  I. 

■  the  original  of  our  ideas, 
their  various  divisions,  and 
the  manner  in  which  they 
pontribott  to  the  increase 
of  knowledge  ;  with  a  phi- 
losophical account  of  the 
rise,  ]  i  d  nature  of 

human  language. 

BOOK  II. 

fthe  grounds  of  human  judg- 
ment, the  doctrine  of  pro- 
ions,  their  use  in  rea- 
soning, &  division*  into  self 
evident  and  demonstrable. 


book  nr. 

Of  reasoning  and  demonstra- 
tion, with  their  application 
tothe  investigation  of  know- 
ledge, and  the  common  af- 
fairs of  life. 

book  iv. 

Of  the  methods  of  invention, 
and  science,  where  the  se- 
veral degrees  of  evidence 
are  examined,  the  notion  of 
certainty  is  fixed  and  stated, 
and  the  parts  of  knowledge 
in  which  it  may  be  attain- 
ed,  demonstrated  at  large. 


DESIGNED    PARTICULARLY   FOR 

Young  Gentlemen  at  the  University; 

tfD  TO  PREPARE  THE  WAY  TO  THE  STUDY  OF 
PHILOSOPHY  AND  THE  MATHEMATICS. 

BY  WILLIAM  DUNCAN, 

a 

Professor  of  Philosophy  in  Marishal  College  y  Aberdeen^ 


Doctrina   sed  vim  promovet  insitam  ; 
Rectique  cultus  pectora  roborant Hok, 


NEW-YORK  : 

PHINTED  BY   L.   NICHOLS,    &  C©. 
FOR   RyERT  DUrCKIXCK*   BOOKSELLER. 


\o* 


&1 


0> 


T©  THE 


RIGHT  HONORABLE 


STEPHEN  POYNTZ;  Esq. 

SIR, 

IF  I  take  this  opportunity  of  publishing  to  the 
world  the  efteem  I  have  for  a  character  to  which 
learning  is  fo  greatly  indebted,  I  hope  you  will  not 
think  yourfelf  injured  by  fuch  a  declaration  from  a 
man  that  honors  you,  and  who  looks  upon  the  liber- 
ty of  putting  the  following  work  under  your  patron- 
age, as  one  of  the  happy  incidents  of  his  life. 

From,  the  fir  ft  moment  I  formed  the  defign  of  it, 
I  had  it  in  my  thoughts  to  acldrefs  it  to  you  ;  and 
indeed  what  could  be  more  natural,  tl^an  that  I 
(hould  be  ambitious  of  infcribing  a  treai  the 

elements  of  philofophy,  to  one,  who  has  10  emi- 
nently diftinguifhed  himfelf  by  his  extenfive  know- 
ledge in  that,  as  well  as  all  the  other  branches  of 
human  learning  ? 

Your  great  abilities  in  every  kind,  have  deferv- 
edly  recommended  you  to  the  notice  of  your  king 
and  country,  and  occasioned  your  being  courted  and 
importuned  to  accept  of  thofe  high  offices  of  ftate, 
which  others  purfue  with  fo  much  eagernefs,  and 
find  it  often  difficult  to  obtain,  by  all  the  arts  and 
endeavors  of  ambition.  Nor  have  your  talents  bee  a 
confined  to  the  view  of  your  country  alone.  Fo- 
reign nations  have  feen  and  admired  you,  and  ftill 
fpeak  with  the  greateft  applaufes  of  your  wife  and 
able  conduft,  when  it  was  your  province  to  a£t  as 
a  Britifh  minifter  abroad. 


4  DEDICATION. 

But  the  qualities  of  a  great  flatefman  are  not 
thofe  alone  by  which  you  have  rendered  yourfelf  il- 
luftvious.  The  virtues  of  private  life  no  lefs  actu- 
ate and  adorn  your  whole  behavior,  and  add  a  new 
dignity  to  the  high  ftation  to  which  your  merit  has 
raifed  you.  Affability,  complacency  of  manners, 
and,  above  all,  an  extenfive  humanity  and  benevo- 
lence, which  takes  pleafure'in  doing  good,  are  dis- 
tinguishing parts  of  your  character,  and  have  con- 
tributed no  lefs  than  your  other  extraordinary  en- 
dowments, to  that  univerfal  acknowledgement  which 
is  paid  you  by  your  country. 

'  Tjiat  you  may  long  live  to  be  an  ornament  and. 
bleffing  to  the  nation,  and  to  enjoy  the  pleafure 
which  arifes  from  a  confcioufnefs  of  the  efteem  and 
approbation  of  all  good  men,  is  the  fincere  and  hear- 
ty prayer  of, 

Six, 

Tquv  most  obliged)  and  most  obedient 

Humble  Servant, 

Z8X.  Duncan, 


%%  m 


C  5  ] 

3[ntromictton. 

Sec.  l,.„Importance  of  the  Knowledge  of  Ourseh:o* 

OF  all  the  human  sciences,  that  concerning  man  is 
certainly  the  most  worthy  of  man,  and  the  most 
necessary  part  of  knowledge.  We  find  ourselves  in  this 
•world  surrounded  with  a  variety  of  objects  :  we  have 
powers  and  faculties  fitted  to  deal  with  them,  and  arc 
happy  or  miserable  in  proportion  as  we  know  how  to 
frame  a  right  judgment  of  things,  and  shape  our  actions 
agreeably  to  the  circumstances  in  which  we  are  placed. 
No  study,  therefore,  is  more  important  than  that  which 
introduces  us  to  the  knowledge  of  ourselves.  Hereby 
we  become  acquainted  with  rhe  extent  and  capacity  of 
the  human  mind  ;  and  learning  to  distinguish  what  ob- 
jects it  is  suited  to,  and  in  what  manner  it  must  proceed 
in  order  to  compass  its  ends,  we  arrive  by  degrees,  at 
that  justness  and  truth  of  understanding,  which  is  the 
great  perfection  of  a  rational  being. 
Sec.  II.... Different  gradations  of  Perfection  in  Things* 

If  we  look  attentively  into  things,  and  survey  th 
in  their  full  extent,  we  see  them  rising  one  above  ano- 
ther in  various  degrees  of  eminence.  Among  the  ina- 
nimate parts  of  matter,  some  exhibit  nothing  worthy 
our  attention  :  their  parts  seem  as  it  were  jumbled 
together  by  mere  chance%nor  can  we  discover  any  beau- 
ty, order,  or  regularity  in  their  composition.  In  others, 
•we  discern  the  finest  arrangement,  and  a  certain  ele- 
gance of  contexture,  that  makes  us  afRxto  tlnm  a  no- 
tion of  worth  and  excellence.  Thus  metals,  and  pre- 
cious stones,  are  conceived  as  far  surpassing  those  un- 
formed masses  of  earth,  that  lie  every  where  exposed 
to  view.  If  we  trace  nature  onward,  and  pursue  her 
through  the  vegetable  and  animal  kingdoms,  we  find 
her  still  multiplying  her  perfections,  and  rising,  by  a 
just  gradation,  from  mere  mechanism  to  perception, 
and  from  perception,  in  all  its  various  degrees,  to  rea- 
son and  understanding. 

Sec.   111. ...Usefulness  of  Culture,  and  particularly  of 
the  Study  of  Logic. 

But  though  reason  be  the  boundary  by  which  man  is 
A  3 


vi  INTRODUCTION, 

distinguished  from  the  other  creatures  that  surround  him, 
yet  we  are  far  from  finding  it  the  same  in  all.  Nor  is  this 
inequality  to  be  wholly  ascribed  to  the  original  make 
of  men's  minds,  or  the  difference  of  their  natural  en- 
dowments. For  if  we  look  abroad  into  the  several  na- 
tions of  the  world,  some  are  over-run  with  ignorance  and 
barbarity  ;  others  flourish  in  learning  and  the  sciences  ; 
and  what  is  yet  more  remarkable,  the  same  people  have 
indifferent  ages,  been  distinguished  by  these  very  op- 
posite characters.  It  is  therefore  by  culture,  and  a  due 
application  of  the  powers  of  our  minds,  that  we  increase 
their  capacity,  and  carry  human  reason  to  perfection. 
"Where  this  method  is  followed,  knowledge  and  strength 
of  understanding  never  fail  to  ensue  ;  where  it  is  neg- 
lected, we  remain  ignorant  of  our  own  worth  ;  and 
those  latent  qualities  of  the  soul,  by  which  she  is  fitted 
to  survey  this  vast  fabric  of  the  world,  to  scan  the  hea- 
vens, and  search  jnto  the  causes  of  things,  He  buried  in 
darkness  and  obscurity.  No  part  of  knowledge,  there- 
fore, yields  a  fairer  prospect  of  improvement,  than 
that  which  takes  account  of  the  understanding,  exa- 
mines its  powers  and  faculties,  and  shews,  the  ways  by 
-which  it  comes  to  attain  its  various  notions  of  things. 
This  is  properly  the  design  of  Logic,  which  may  be  just- 
ly stiled  the  history  of  the  human  mind,  inasmuch  as  it 
traces  the  progress  of  our  knowledge,  from  our  first 
and  simple  perceptions,  through  all  their  different  com- 
binations, and  all  those  numerous  deductions  that  result 
from  variously  comparing  them  one  with  another.  It  is 
thus  that  we  are  let  into  the  natural  frame  and  contex- 
ture of  our  own  minds,  and  learn  in  what  manner  we 
ought  to  conduct  our  thoughts,  in  order  to  arrive  at 
truth,  and  avoid  error.  We  see  how  to  build  one  dis- 
covery upon  another,  and,  by  preserving  the  chain  of 
reasonings  uniform  and  unbroken,  to  pursue  the  rela- 
tions of  things  through  all  their  labyrinths  and  wind- 
ings, and  at  length  exhibit  them  to  the  view  of  the  soul, 
ytith  all  the  advantages  of  light  and  conviction. 

Sec.  IV. ...Operations  of  the  Mind, 

But  as  the  understanding,  in  advancing  from  one 


INTRODUCTION.  vii 

part  of  knowledge  to  another,  proeeeds  by  a  just  gra- 
dation, and  exerts  various  acts,  according  to  the  diifer- 
ent  progress  it  has  made,  logicians  have  been  careful 
to  note  these  several  steps,  and  have  distinguished  them 
in  their  writings  by  the  name  of  the  operations  of  the 
mind.  These  they  make  four  in  number,  and  agreeably 
to  that  have  divided  the  whole  system  of  logic  into  four 
parts,  in  winch  these  acts  are  severally  explained,  and 
the  conduct  and  procedure  of  the  mind,  in  its  different 
stages  of  improvement,  regulated  by  proper  rules  and 
observations.  Now,  in  order  to  judge  how  far  logicians 
have  followed  nature,  in  this  distinction  of  the  powers 
of  the  understanding,  let  us  take  a  short  view  of  the 
mind,  and  the  manner  of  its  progress,  according  to  the 
experience  we  have  of  it  in  ourselves,  and  see  whi- 
ther the  chain  of  our  own  thoughts  will  without  con- 
straint lead  us. 

Sec.  V '.*.•  Perception* 

First,  then,  we  find  ourselves  surrounded  with  a  va- 
riety of  objects,  which,  acting  differently  on  our  senses, 
convey  distinct  impressions  into  the  mind,  and  thereby 
rouse  the  attention  and  notice  of  the  understanding. 
By  reflecting,  too,  on  what  passes  within  us,  we  become 
sensible  o£  the  operations  of  our  own  minds,  and  at- 
tend to  them  as  a  new  set  of  impressions.  But  in  all  this 
there  is  only  bare  consciousness.  The  mind,  without 
proceeding  any  farther,  takes  notice  of  the  impressions 
that  are  made  upon  it,  and  views  things  in  order  as 
they  present  themselves  one  after  another.  This  atten- 
tion of  the  understanding  to  the  objects  acting  upon  it, 
whereby  it  becomes  sensible  of  the  impressions  ther 
make,  is  called,  by  logicians,  perception  ;  and  the  no- 
tices themselves,  as  they  exist  in  the  mind,  and  are 
there  treasured  up  to  be  the  materials  of  thinking  and 
knowledge,  are  distinguished  by  the  name  of  ideas* 

Sec.    VI... •Judgment. 

But   the  mind  does  not  always  rest  satisfied  in  the 

bare  view  and  contemplation  of  its  ideas.       It  is  of  a 

more  active  and  busy  nature,  and  likes  to  be  assembling 

them  together,  and  comparing  them  one  with  another. 


viii  INTRODUCTION. 

In  this  complicated  view  of  things,  it  readily  discerns, 
that  some  agree  and  others  disagree,  and  joins  or  sepa- 
rates them  according  to  this  perception.  Thus,  upon 
comparing  the  idea  of  two  added  to  two,  with  the  idea 
of  four,  we,  at  first  glance,''  perceive  their  agreement, 
and  thereupon  pronounce  that  two  and  two  are  equal 
to  four.  Again,  that  white  is  not  black,  that  five  is  less 
than  seven,  are  truths  to  which  we  immediately  assent, 
as  soon  as  we  compare  those  ideas  together.  This  is  the 
first  and  simplest  act  of  the  min^l,  in  determining  the 
relation  of  things,  whe$,  by  a  bare  attention  to  its 
own  ideas,  comparing  any  two  of  them  together,  it 
can  at  once  see  how  far  they  are  connected  or  disjoin- 
ed. The  knowledge  thence  derived  is  called  intuitive, 
as  requiring  no  pains  or  examination;  and  the  act  of 
the  mind  assembling  its  ideas  together,  and  joining  or 
disjoining  them,  according  to  the  result  of  its  fiercep* 
tions,  is  what  logicians  term  judgment. 

Sec.  V 'II.... Reasoning, 

Intuition  affords  the  highest  degree  of  certainty;  it 
breaks  in  with  an  irresistible  light  upon  the  undemand- 
ing, and  leaves  no  room  for  doubt  or  hesitation..  Could 
we  in  all  cases,  by  thus  putting  two  ideas  together,, 
discern  immediately  their  agreement  or  disagreement, 
we  should  be  exempt  from  error,  and  all  its  fatal  con- 
sequences. But  it  so  happens,  that  many  of  our  ideas 
are  of  such  a  nature,  that  they  cannot  be  thus  examined 
in  concert,  or  by  any  immediate  application  one  to 
another ;  and  then  it  becomes  necessary  to  find  out  some 
other  ideas  that  will  admit  of  this  application,  that  by 
means  of  them  we  may  discover  the  agreement  or  dis- 
agreement we  search  for.  Thus  the  mind  wanting  to 
know  the  agreement  or  disagreement  in  extent  between 
two  enclosed  fields,  which  it  cannot  so  put  together  as 
to  discover  their  equality  or  inequality  by  an  immedi- 
ate comparison,  casts  about  for  some  intermediate  idea, 
which,  by  being  applied  first  to  the  one,  and  then  to 
the  pther,  will  discover  the  relation  it  is  in  quest  of. 
Accordingly  it  assumes  some  stated  length,  as  a  yard,  &c» 
and  measuring  the  fields  one  after  the  other,  comes  by 


INTRODUCTION.  i* 

that  means  to  the  knowledge*of  the  agreement  or  dis- 
agreement in  question.  Tjie  intervening  ideas  made  use 
of  on  these  occasions,  are  called  proofs  ;  and  the  exer- 
cise of  the  mind  in  finding   them    out,   and   applying 
them  for  the  discovery  of  the  truths  it  is  in  search  of,  is 
■what  we  term  reasoning.  And  here  let  it  be  observed, 
that  the  knowledge  gained  by  reasoning  is  a  deduction 
from  our  intuitive  perceptions,  and  ultimately  founded 
on  them.     Thus  in  the  case  before  mentioned,  having 
found  by  measuring,  that  one  of  the  fields  makes  three- 
score square   yards,  -fnd  the  other  only  fifty-five,   we 
thence    conclude,  that  the  firft  field  is  larger  than  the 
second.     Here  the  two  first  perceptions  are  plainly  in- 
tuitive, and  gained  by  an' immediate  application  of  the 
measure  of  a  yard  to  the  two  fields,  one  after  another; 
The   conclusion,    though   it  produces  no  less    certain 
knowledge,  yet  differs  from  the  others  in  this,  that  it 
is    not  obtained  by    an   immediate  comparison  of  the 
ideas  contained  in  it,  one  with  another,  bu4  is  a  deduc- 
tion from  the  two  preceding  judgments,  in  which  the 
ideas   are    severally   compared  with  a  third,  and  their 
relation  thereby  discovered.     We  see,  therefore,  that 
reasoning   is    a    much  more    complicated  act   of  the 
mind   than    simple  judgment,  and  necessarily  presup- 
poses it,    as  being  ultimately   founded  on  the   percep- 
tions thence  gained,   and  implying  the  various  compa- 
risons of  them  one   with   another.     This  is  the  great 
exercise  of  the  human  faculties,    and  the  chief  instru- 
ment by  which  we  push  on  our  discoveries,  and  enlarge 
our  knowledge.     A   quickness  of  mind  to  find  out  in-    " 
termediate  ideas,  and  apply  them  skilfully  in  determin- 
ing the  relations  of  things,  is  one  of  the  principal  dis- 
tinctions among  men,  and  that  which  give  some  so  re- 
markable a  superiority  over  others,  that  we  are  apt  to 
look  upon  them  as  creatures  of  another  species. 

Sec.  VUL...Method. 

Thus  far  we  have  traced  the  progress  of  the  mind  in 
thinking,  and  seen  it  rising  by  natural  and  easy  steps 
from  its  first  and  simple  perceptions,  to  the  exercise 
•f  its  highest  and  most  distinguishing  faculty.    Let  us 


x  INTRODUCTION. 

now  view  it  in  another  light,  as  enriched  with  know- 
ledge, and  stored  with  a  variety  of  discoveries,  acquired 
by  a  due  application  of  its  natural  powers.      It  is  obvi- 
ous to  consider  it  in  these  circumstances,  as  taking  a 
general  survey  of  its  whole  stock  of  intellectual  ac- 
quisitions,   disposing   them   under   certain  heads   and 
classes,  and  tying  them  together,  according  to  those 
connexions  and  dependencies  it  discerns  between  them* 
It   often   happens,  in   carrying  on  our  enquiries  from 
subject  to  subject,  that  we  stumble  upon  unexpected 
truths,  and  are  encountered  by  discoveries-  which  our 
present  train  of  thinking  gave  no  prospect  of  bring- 
ing  in  our  way.     A  man  of  clear  apprehension,  and 
distinct  reason,  who,  after  due  search  and  examina- 
tion, has  mastered  any  part  of  knowledge,  and  even 
made   important  discoveries  in  it,  beyond  what  he  at 
first  expected,  will  not  suffer  his  thoughts  to  lie  jum- 
bled together  in  the  same  confused  manner  as  chance 
offered  them;  he  will  be  for  combining  them  into  a  re- 
gular system,  where  their  mutual  dependence  may  be 
easily  traced,  and   the  parts  seem  to  grow  one  out  of 
another.     This  is  that  operation  of  the  mind,  known 
by  the  name  of  disposition  or  method,  and  comes  in  the 
last  in  order,  according  to  the  division  of  the  logicians, 
as  presupposing  some  tolerable  measure  of  knowledge, 
before  it  can  have  an  opportunity  of  exerting  itself  in 
any  extensive  degree. 

Sec.  IX.... Percept ion  and  Judgment  terms  of  a  very 
extensive  signification. 

We  see,  then,  that  this  fourfold  distinction  of  the 
powers  of  the  mind,  in  perception,  judgment,  reason- 
ing, and  disposition,  as  well  as  the  order  in  which  they 
are  placed,  have  a  real  foundation  in  nature,  and  a  rise 
from  the  method  and  procedure  of  our  own  thoughts. 
It  is  true,  there  are  many  other  actions  and  modifica- 
tions of  the  understanding,  besides  those  above  men- 
tioned, as  believing,  doubting,  assenting,  Sec.  but  these 
are  all  implied  in  the  act  of  reasoning,  in  the  like  man- 
ner, as  comprehending,  abstracting,  remembering,  may 
be  referred  to  tbe  first  operation  of  the  mind,  or  per- 


INTRODUCTION.  » 

Caption.     This  will  appear  more  fully   in  the  sequel, 
ivhen  we  come  to  handle  the  several  parts  of  logic  sepa- 
rately :  at  present  we  shall  content  ourselves  with  this 
general  account  of  things  ;  only  it  seems  necessary  to 
observe,  that  perception  and  judgment,  in  the  propriety 
of  the   English  tongue,   have  a  much  more  extensive 
signification  than  logicians  commonly  allow  them.    We 
not  only  perceive  the  ideas  in  our,  own  minds,  but  we 
are  said  also  to  perceive  their  agreement  or  disagree- 
ment ;  and  hence  arise  the  common  phrases  of  intuitive 
perceptions,  perceptions  of  truth,  and  of  the  justness 
of  arguments  or  proofs;  where  it  is  manifest,  that  the 
word  is  applied  not  only  to  our  judgments,  but  also  to 
our  reasonings.      In   a  word,  whatever  comes  under 
the  view  of  the  mind,  so  as  to  be  distinctly  represented 
and  taken  notice  of,    whether  an  idea,    proposition, 
chain  of  reasoning,  or  the  order    and   connexion   of 
things,  is  thereby  rendered  an   object  of  perception, 
and  gives  employment  to  this  first  and  most  simple  of 
our  faculties.     In  like  manner,  the  vr  oi&,  judgment,  is 
seldom,  in  common  discourse,  confined  to  obvious  and 
self-evident  truths.  It  rather  signifies  those  conjectures 
and  guesses  that  we  form,  in  cases  which  admit  not  of 
undoubted  certainty,  and  where  we  are  left  to  deter- 
mine by  comparing  the  various  probabilities  of  thing?. 
Thus  a  man  of  sagacity  and  penetration,  who  sees  far 
into  the  humours  and  passions  of  mankind,  and  seldom 
mistakes  in  the  opinions  he  frames  of  characters  and 
actions,  is  said  to  judge  well,  or  think  judiciously.   For 
these  reasons,  it  might  not  be  improper  to  change  the 
common  names  of  die  two  first  operations  of  the  mind, 
calling  the  one  simjyle  apprehension^  and  the  other  ihtuU 
tion  ;  which  two  words  seem  better  to  express  their  na- 
ture, and  the   manner  in   which  they  are  conversant 
about  their  several  objects.     This  accuracy  of  distin- 
guishing, where  there  is  any  the  least  difference,  is  in 
a  peculiar  manner  necessary  in  a  treatise  of  logic,  as  it 
is  the  professed  design  of  that  science,  to  teach  us  how 
to  form.,  clear  and  distinct  notions  of  things,  and  there- 
by avoid  being  misled  by  their  similitude  or  rcsem* 
blance. 


*ii  INTRODUCTION. 

See*  ¥L.t»*Logic  divided  into  Four  Parts:     Its  Useful" 
ness  and  Excellency* 
Having  thus  given  a  general  idea  of  the  four  opera- 
tions of  the  mind,  and  traced  their  connection  and  de- 
pendence upon  one  another,  I  would  next  observe,  that 
in  consequence  of  this  division  of  the  powers  of  the  un- 
derstanding, logic  is  also  divided  into  four  parts,  which 
treat  severally  of  these  acts,  and  give  rules  and  direc- 
tions for  their  due  conduct  and  regulation.     The  ope- 
rations themselves  we  have  from  nature.;    but  how  to 
exert  tbem  justly,    and  employ  them   with  advantage 
in  the  search  of  truth,  is  a  knowledge  that  may  be  ac- 
quired by  study  and  observation.   It  is  certain,  that  we 
meet  with  false  reasonings  as  well  as  just.   Some  men 
are  distinguished  by  an  accuracy  of  thinking,    and   a 
happy  talent  of   unravelling  and  throwing  light  upon 
the  most  obscure  and  intricate  subjects.      Others  con- 
found the  easiest  speculations  ;    their   understandings 
seem  to  be  formed  awry,  and  they  are  incapable  of  ei- 
ther conceiving  clearly   themselves,    or    making  their 
thoughts  intelligible  to  others.  If  then  we  set  ourselves 
carefully  to  observe  what  it  is  that  makes  the  one  suc- 
ceed so  well,   and  how  the  others  come   to   miscarry, 
these  remarks  will  furnish  us  with  an  art  of  the  highest 
use  and  excellency  in  the  conduct  of  life.  Now  this  is 
the  precise  business  of  logic — to  explain  the  nature  of 
the  li'iman  mind,  and  the  proper  manner  of  conducting 
its  several  powers,    in  order  to  the  attainment  of  truth, 
and  knowledge.  It  lays  open  those  errors  and  mistakes 
we  are  apt  through  inattention  to  run  into,  and  teach- 
es us  how  to  distinguish  between  truth,  and  what  car- 
ries only  the  appearance. of  it.   By  this  means,  we  grow 
acquainted  with  the  nature  and   force    of   the  under- 
standing, see  what  things  lie  within  its  reach,    where 
we  may  attain  certainty  and  demonstration,  and  when 
we  must  be  contented  with  bare  probability.       xhese 
considerations  sufficiently    evince  the    usefulness  and 
benefit  of  this  science,  which  ought  to  be  established  as 
the  foundation  and  ground-work  of  all  our  other  know- 
ledge, if   we  really  wish   to  succeed  in    our  enquiries. 
But  we  shall  now  proceed  to  treat  of  its  parts  separate- 
ly, according  to  the  division  given  of  them  above. 


ELEMENTS  OF  LOGIC. 

OF  SIMPLE  APPREHENSION, 
OR  PERCEPTION, 


C&ap.  I. 

t)F  THE  ORIGINAL  OF  OUR  IDEAS* 

ooooooooooooooooo 

Sec,  I Simple  Apprehension  and  Ideas, 

THE  first  thinf^  we  observe,  when  we  take  a  vietfr 
of  what  passes  within  us,  is,  that  we  are  capable 
of  receiving  impressions  from  a  variety  of  objects  ;  that 
distinct  notices  are  thereby  conveyed  into  the  under- 
standing ;  and-that  we  are  conscious  of  their  being 
there.  This  attention  of  the  mind  to  the  objects  acting 
upon  it,  is  what  we  c:di  simple  apprehension,  and  is,  in 
fact,  the  mind  itself  taking  a  view  of  things,  as  repre- 
sented to  it  by  its  own  consciousness.  It  is  by  this 
means  that  we  come  to  be  furnished  with  all  those 
ideas  about  which  our  thoughts  are  employed.  For  be-* 
ing  sensible  of  the  impressions  made  upon  us,  aiul  at- 
tending to  the  perceptions  they  bring,  we  can  renew 
them  again  upon  occasion,  even  when  the  objects  that 
first  produced  them  are  removed*  Now,  our  ideas  are 
nothing  else  but  these  renewed  representations  of  what 
■we  have  at  any  time  perceived  and  felt,  by  means  of 
which  things  are  again  brought  under  the  view  of  the 
mind,  and  seem  to  have  a  kind  of  existence  in  it.  It 
is  true,  we  can  upon  "many  occasions  combine  our  ideas 
variousiy  together,  and  thereby  form  to  ourselves  re- 
presentations of  tilings  that  never  had  an  existence  in 
nature,  as  when  we  fancy  a  centaur,  or  a  golden  moun- 
tain ;  but  it  is  Still  certain,  that  the  original  ideas, 
ktattfe  °f  which  these  are  made,  are  such  as  have  been 
^28kveyed  into  the  xniiid  bv  -some  former  impressions,- 

B 


14  DTJNCAN':S  ELEMENTS 

Ir  remains  therefore  to  enquire  how we  come  'by  our. 
first' notions  and  perception's  of  things.  Whence  doe3 
the  understanding  derive  these  original  impressions  and 
characters,  which  it  can  combine  in  so  many  differens 
ways,  and  represent  to  itself  under  such  infinite  varie- 
ties ?  To  this  I  answer,  that  if  we  attend  carefully  to 
Tvhat  'passes  in  our  minds,  we  shall  observe  two  inlets  of 
knowledge,  from  whence,  as  from  two  fountains,  the  un- 
derstanding is  supplied  with  all  the  materials  of  think- 
ing. 

Sec.  II... *All  our  original  Ideas  derived  either  from 
Sensation, 
Rrst,  outward  objects,  acting  upon  otir  senses, 
rouse  in  us  a  variety  of  perceptions,  according,  to  the 
different  manner  in  which  they  affect  us.  It  is  thus, 
that  we  acquire  ideas  of  light  and  darkness,  heat  and 
cold,  sweet  and  bitter,  and  all  those  other  impressions 
which  we  term  sensible  qualities.  This  great  source 
and  inlet  of  knowledge  is  commonly  distinguished  by 
the  name  of  sensation,  as  comprehending  all  the  noticed 
conveyed  into  the  mind3  by  impulses  made  upon  the 
organs  of  sense* 

See.  III.. ..Or  Reflection* 
But  these  ideas,   numerous  as  they  are,    are  wholly 
derived   to  us   from    without  :   there  is  therefore    yeff 
another  source  of   impressions,  arising  from  the  mind's 
attention  to  its  own  acts,  when,  turning  in  Wards  upoh- 
itself,    it  takes  a  view  of  the  perceptions  that  are  lodg- 
ed there,    and  the  various  ways  in  which  it  employs  it- 
self about  them.   For  the  ideas  furnished  by  the  senses, 
give  the  mind  an  opportunity  of  exerting  its  several 
powers  ;    and   as   all  our   thoughts,    under    whatever 
form  they   appear,   are    attended  with  consciousness, 
lience  the  impressions  they  leave,  when  we  come  to  turn 
the  eye  of  the  soul  upon  them,  enrich  the  understanding 
"With  a  new  set  of  perceptions,  no  less  distinct  than  those 
conveyed  in  by  the  senses.   Thus  it  is  that  we  get  ideas 
of  thinking,  doubting,  believing,  willing)   <kc.  which 
are  the  different  acts  and  workings  of  our  minds,  repre- 
sented to  us  by  our  own  consciousness.      This  second 
source  of  ideas  is  called  reflection,  and  evidently  ptesup* 


OF  LOGIC.  15 

poses  sensation  ;  as  the  impressions  it  furnishes  are  only 
q£  the  various  powers  of  the  understanding,  employed 
about  perceptions  already  in  the  mind. 

Sect.  IV Rise  and  Progress  of  Human  Knowledge* 

These  considerations,  if  we  duly  attend  to  them,  will 
'give  us  a  clear  and  distinct  view  of  the  natural  proce- 
dure  of  the  human  intellect,  in  its  advances  to  know- 
ledge. We  can  have  no  perception  of  the  operations 
of  our  own  minds,  until  they  are  exerted  ;  nor  can  they 
be  exerted  before  the  understanding  is  furnished  with, 
ideas  about  which  to  employ  them  :  and  as  these  ideas, 
that  give  the  first  employment  to  our  faculties,  are  evi- 
dently the  perceptions  of  sense,  it  is  plain,  that  all  our 
knowledge  must  begin  here.  This,  then,  is  the  first 
capacity  of  the  human  mind,  that  it  is  fitted  to  receive* 
the  impressions  made  upon  it  by  outward  objects  affect- 
ing the  senses;  which  impressions,  thus  derived  into 
the  understanding,  and  there  lodged,  for  the  view  of  the 
soul,  employ  it  in  various  acts  of  perceiving,  remember- 
ing, considering,  Sec.  all  which  are  attended  with  am 
internal  feeling  and  consciousness.  And  this  leads  us 
to  the  second  step  the  mind  takes  in  its  ^progress  to- 
wards knowledge,  viz.  that  it  can,  by  its  own  consci- 
ousness, represent  to  itself  these  its  several  workings 
and  operations,  and  thereby  furnish  the  understanding 
with  a  new  stock  of  ideas.  From  these  simple  begin- 
nings, all  our  discoveries  take  their  rise:  for  the  mind, 
thus  provided  with  its  original  characters  and  notices  of 
things,  has  a  power  of  combining,  modifying,  and  ex- 
amining them  in  an  infinite  variety  of  lights,  by  which 
means  it  is-eiiabled  to  enlarge  the  objects  of  its  percep- 
tion, and  finds  itself  possessed  of  an  inexhaustible  stock 
of  material-!.  It  is  in  the  various  comparison  of  these 
ideas,  according  to  such  combinations  of  them  as  seem 
best  to  suit  its  ends,  that  the  understanding  exerts  it- 
self in  the  arts  of  judging  and  reasoning,  by  which  the 
capacious  mind  cf  man  pushes  on  its  views  of  things, 
adds  discovery  to  discovery,  and  often  extends  its 
thoughts  beyond  the  utmost  bounds  of  the  universe. 
Thus  we  see,  as  it  were,  at  one  glance,  the  whole  pro- 
gress of  the  soul,  from  the  very  hrst  dawnings  of  per- 


16  DUNCAN'S  ELEMENTS 

ception,  till  it  reaches  the  perfection  of  human  know- 
ledge;  nor  shall  we,  among  all  its  vast  stock  of  disco- 
veries, or  that  infinite  variety  of  conceptions  whereof 
they  consist,  be  able  to  find  one  original  idea  which  is 
not  derived  from  sensation  or  reflection,  or  one  com- 
plex idea  which  is  not.  made  up  of  those  original  ones. 
Sec.  V.  Division  of  our  Ideas  into  Simple  and  Complex* 
Having  thus  shown  how  the  mind  comes- to  be  first 
furnished  with  ideas,  we  shall  next  proceed  to  the 
consideration  of  the  ideas  themselves,  and  endeavour 
to  give  such  an  account  of  them,  as  will  best  serve  to? 
explain  their  several  appearances,  and  the  manner  in 
which  they  are  formed.  It  is  evident,  from  what  has 
been  said  above,  that  they  all  fall  naturally  under 
these  two  heads  :  first,  those  original  impressions  that 
are  conveyed  into  the  mind  by  sensation  and  reflection,' 
and  which  exist  there,  simple,  uniform,  and  without 
any  shadow  of  variety.  Secondly^  those  more  complex 
notions  of  things,  that  result  from  the  various  com- 
binations of  our  simple  ideas,  whether  they  are  con- 
ceived to  exist  of  themselves,  in  any  particular  subject, 
or  are  united  and  joined  together  by  the  mind  enlarg- 
ing its  conceptions  of  things,  and  pursuing  the  ends 
and  purposes  of  knowledge.  These  two  classes  com- 
prehend our  whole  stock  of  ideas  ;  and,  when  consi- 
dered separately,  in  that  order  wherein  they  most*  na- 
turally seem  to  offer  themselves  to  our  thoughts,  will, 
I  hope,  give  such  a  view  of  the  conduct  and  manner 
of  the  mind,  as  may  contribute  not  a  little  to  intro- 
duce us  to  an  acquaintance  with  ourselves,  and  make 
us  sensible  pf  the  capacity  and  extent  of  the  human 
intellect.  We  proceed,  therefore,  to  a  more  particular 
account  of  this  division  of  our  ideas. 

Cjmp.  n. 

Of    SIM  PLE    IDEAS. 

Sec.   I..,.. Simple  Ideas  what, 

THE  first  class  of  our  ideas  are  those  which  I  dis- 
tinguish by  the.  name  of  simple  perception  ;  be- 


OF  LOGIC.  17 

cause  they  exist  in  the  mind  under  one  uniform  appear- 
ance without  variety  or  composition.  For  though  ex- 
ternal objects  convey  at  once  into  the  understanding* 
many  different  ideas,  all  united  together,  and  making 
as  it  were  one  whole  :  yet  the  impressions  themselves  are 
evidently  distinct,  and  are  conceived  by  the  mind,  each 
under  a  form  peculiar  to  itself.  Thus  the  ideas  of  co- 
lour, extension,  and  motion,  may  be  taken  in  at  one  and 
the  same  time,  from  the  same  body  ;  yet  these  three 
perceptions  are. as  distinct  in  themselves,  as  if  they  all 
proceeded  from  different  objects,  or  were  exhibited  to 
our  notice  at  diifereni  times.  We  are  therefore  care- 
fully to  distinguish  between  our  simple  and  primitive 
conceptions,  and  those  different  combinations  of  them, 
which  are  ofcen  suggested  to  the  mind  by  single  ob- 
jects acting  upon  it.  The  first  constitute  our  original 
notices  of  things,  and  are  not  distinguishable  into  dif- 
ferent ideas,  bur  enter  by  the  senses  simple  and  unmix- 
ed. They  are  ajso  the  materials,  out  of  which  all  the 
others,  how  complex  and  complicated  soever,  are  form- 
ed ;  and  therefore  ought  deservedly  to  be  looked  on  as 
the  foundation  and  groundwork  of  our  knowledge. 

Sec.   II Simple  Ideas  of  Sensation* 

Now  if  we  take  a  survey  of  these  ideas,  and  their 
several  divisions  and  classes,  we  shall  find  them  all  sug- 
gested to  us,  either  by  our  senses,  or  the  attention  of 
the  mind  to  what  passes  within  itself.  Thus  our  no- 
tices of  the  different  qualities  cf  bodies,  are  all  of  the 
kind  we  call  simple  ideas,  and  may  be  reduced  to  five  ge- 
neral heads,  according  to  the  several  organs  which  are 
affected  by  them.  Colours,  Sec.  and  sounds,  are  con- 
veyed in  by  the  eyes  and  ears  ;  tastes  and  smells  by  the 
nose  and  palate  ;  and  heat,  cold,  solidity,  Sec.  by  the 
touch.  Besides  these,  there  are  others'  which  maxe  im- 
pressions on  several  cf  our  senses,  as  extension,  figure, 
rest,  and  motion,  Sec.  the  ideas  of  which  we  receive 
into  our  minds  both  by  seeing  and  feeling. 

Sec.   111,.,,, Simple.  Ideas  of  Reflexion,  fcrV. 
If  we  next  turn  cur  view  upon  what  passes  within 
ourselves,  we  shall  find  another  set  of  simple  ideas  ari- 
B  2 


18  DUNCAN'S  ELEMENTS 

sing  from  our  consciousness  of  the  acts  and  operations 
of  our  own  minds.  Perception  or  thinking,  and  voli- 
tion or  willing,  are  what  every  man  experiences  in  him- 
self, and  cannot  avoid  being  sensible  of.  I  shall,  only 
observe  further,  that  besides  all  the  above-mentioned 
perceptions,  there  are  others  that  come  into  our  minds 
by  all  t^ie  ways  of  sensation  and  reflexion  ;  such  are  the 
ideas  of  pleasure  and  gain,  power,  existence,  unity,  suc- 
cession, &x.  which  are' derived  into  our  understandings 
both  by  the  action  of  objects  without  us,  and  the  con- 
sciousness of  what  we  feel  within.  It  is  true  some  of 
these  ideas,  as  of  extension  and  duration,  cannot  be  con- 
ceived altogether  without  parts,  nevertheless,  they  are 
justly  ranked  among  our  simple  ideas;  because  their 
parts  "being  all  of  the  same  kind,  and  without  the  mix- 
ture of  any  other  idea,  neither  of  them  can  be  resolved 
into  two  distinct  and  separate  conceptions.  Thus  they 
still  answer  the  definition  given  above,  of  being  one 
uniform  appearance  in  the  mind,  with  variety  or  plural- 
ity. But  to  prevent  confounding  our  simple  ideas  of 
space  and  duration,  with  those  complex  modes  of  them 
marked  out  by  tne  several  measures  commonly  in  use, 
as  yards,  miles,  days,  years,  &x.  it  may  perhaps  be  most 
proper  to  consider  the  least  portions  of  either  whereof 
we  can  form  a  clear  and  distinct  perception,  as  the  sim- 
ple ideas-of  that  kind  out  of  which  all  their  other  modes 
and  combinations  are  formed.  Such  an  instant,  or 
point,  may  be  conceived  to  be  the  same  in  respect  of 
duration  or  space,  as  unity  is  in  respect  of  number  ; 
and  will  serve  best  to  show,  how  by  a  continued  addi- 
tion or  repetition,  our  more  enlarged  and  complex  ideas 
are  made  up. 

Sec.  IV... .Simple  Ideas  have  no  Admission  but  by  the 
proper  Inlets  of  Nature. 
Having  thus  given  a  general  view  of  our  simple 
ideas,  I  have  still  two  observations  to  make  concerning 
them.  The  first  is,  that  they  are  such  as  can  only  be 
conveyed  into  the  mind  by  the  proper  channels  and 
•avenues  provided  by  nature  ;  insomuch  that  if  we  are 
destitute  of  any  of  those  inlets,  by  which  the  impres- 
sions that  produce  tjiem  are  want  to  be  admitted,  all  the 


OF  LOGIC.  1S> 

ideas  thence  arising  are  absolutely  lost  to  us  ;  nor  can 
we,  by  any  quickness  of  understanding,  find  a  remedy 
for  this  want.  A  man  born  blind  is  incapable  of  the 
ideas  of  light  and  colours  ;  in  like  manner  as  one  who 
is  deaf  can  form  no  notion  or  conception  of  sounds. 
Hence  it  appears,  that  these  our  simple  ideas  are  just 
such  as  nature  has  furnished  them,  and  have  no  depen- 
dence on  our  will  ;  we  can  neither  destroy  them  when 
in  the  understanding,  nor  fashion  or  invent  any  nevr 
one,  not  taken  in  by  the  ordinary  means  of  perception. 
So  that  we  here  see  the  utmost  bounds  of  human 
knowledge,  which,  however  mighty  and  enlarged,  can- 
-not  exceed  the  limits  of  those  our  simple  original  ideas, 
and  their  various  combinations. 

Sec.   V....  They  furnish  ample  Materials  of  Knowledge* 

And  this  leads  me  to  the  second  observation  I  pro- 
posed to  make,  which  is,  that  though  the  mind  cannot, 
in  multiplying  its  conceptions  of  things,  advance  one 
step  beyond  the  materials  furnished  it  by  sense  and 
consciousness  ;  yet  as  it  has  a  power  of  combining, 
modifying,  and  enlarging  them,  in  all  the  different 
ways  in  which  they  can  be  put  together,  it  therefore 
finds  itself  in  possession  of  an  inexhaustible  treasure 
of  ideas,  sufficient  to  employ  it  to  the  full  extent  of  all 
its  powers,  and  furnish  matter  for  all  those  various 
opinions,  fancies,  and  views  of  things,  that  make  up 
the  subject  of  its  thoughts  and  contemplations.  Let 
us  but  reflect  upon  the  single  idea  of  unity  or  one,  and 
observe  what  a  variety  of  combinations  are  formed,  by 
continually  adding  it  to  itself;  insomuch  that  the'un- 
derstanding  finds  no  stop  or  boundary,  in  its  progress 
from  number  to  number.  In  what  an  infinity  of  dif- 
ferent lights  may  extension  alone  be  considered  !  what 
limits  can  be  set  to  that  endless  diversity  of  figures, 
which  it  is  in  the  power  of  the  imagination  to  fashion 
and  represent  to  itself?  if  to  these  we  add  those  num- 
berless other  combinations  that' result  from  variously 
compounding  and  comparing  the  rest  of  our  simple 
ideas,  we  shall  have  little  reason  to  complain  of  being 
limited   to  a  scanty  measure  of  knowledge,  or  that  the 


£0  DUNCAN'S  ELEMENTS 

exercise  of  the  human  faculties  is  confined  within  nar- 
row bounds.  But  having  traced  the  progress  of  the 
mind  thro'  its  original  and  simple  ideas,  until  it  begins 
to  enlarge  its  conceptions  by  uniting  and  tying  them 
together  ;  it  is  now  time  to  take  a  survey  of  it  as  thus 
employed  in  multiplying  its  views,  that  we  may  see  by 
what  steps  it  advances  from  one  degree  of  improve- 
ment to  another,  and  how  it  contrives  to  manage  that 
infinite  stock  of  materials  it  finds  itself  possessed  of. 

Sec.  VI....  The  Division  of  complex  Ideas  into  those  &f 
real  Existence,  and  those  framed  by  the  Mind, 

Whoever  attentively  considers  his  own  thoughts, 
and  takes  a  view  of  the  several  complicated  ideas  that 
from  time  to  time  offer  themselves  to  his  understand- 
ing ;  will  readily  observe,  that  many  of  them  are 
such  as  have  been  derived  from  without,  and  suggest- 
ed by  different  objects  affecting  his  perception  ;  others, 
again,  are  formed  by  the  mind  itself  variously  combi- 
ning its  simple  ideas,  as  seems  best  to  answer  those  ends 
and  purposes  it  has  for  the  present  in  view.  Of  the 
first  kind  are  all  our  ideas  of  substance?,  as  of  a  man,  a 
horse,  a  stone,  gold.  Of  the  second  arc  those  arbitrary 
collections  of  things,  which  we  on  many  occasions  put 
together,  either  for  their  usefulness  in  the  commerce  of 
life,  or  to  further  the  pursuit  of  knowledge  :  such  are 
our  ideas  of  stated  lengths,  whether  of  duration  or 
space  ;  as  hours,  months,  miles,  leagues,  &x.  which 
divisions  are  apparently  the  creatures  of  the  mind,  in- 
asmuch as  we  often  find  them  different  in  different 
countries  ;  a  sure  sign  that  they  are  taken  from  no 
certain  and  invariable  standard  in  nature.  Many  of 
our  ideas  of  human  actions  may  be  also  referred  to 
this  head  ;  as  treason,  incest,  manslaughter,  &c.  which 
complex  notions  we  do  not  always  derive  from  an  actual 
'view  of  what  these  words  describe,  but  often  from  com- 
bining the  circumstances  of  them  in  our  minds,'  or, 
which  is  the  most  usual  way,  by  hearing  their  names 
explained,  and  the  ideas  they  stand  for  enumerated. 
These  two  classes  comprehend  all  our  complex  con- 
ceptions, it  being  impossible  to  conceive  any  that  are 


OF  LOGIC.  21 

not  cither  suggested  to  the  understanding  "*by  some 
real  existences,  or  formed  by  the  mind  itself  arbitrarily 
uniting  and  compounding  its  ideas.  We  shall  treat  of 
each  in  order. 


C&ap.  in. 



OF  OUR  IDEAS  OF  SUBSTANCES. 

Sec.  I.... Ideas   of  Substances y  Collections  of  Simple 
IdeaSy  held  together  by  some  unknown  support, 

THE  first  head  of  complex  ideas  mentioned  in  the 
foregoing  chapter,  is  that  of  substances^  -which  I 
choose  to  handle  before  the  other  ;  because,  as  will  af- 
terwards appear,  the  notices  derived  from  this  source 
very  much  help  us  in  forming  those  arbitrary  collec- 
tions, which  make  up  the  second  division.  For  in  many 
ef.  them  we  take  our  hints  from  the  reality  of  things, 
and  combine  ideas  that  actually  exist  together,  though 
often  with  an  exclusion  of  others,  as  will  be  explained 
when  we  come  to  treat  of  abstract  and  universal  notions. 
It  has  been  already  observed,  that  the  impressions  con- 
veyed into  the  understanding  from  external  objects, con- 
sist for  the  most  part  of  many  different  ideas  joined  to- 
gether, which  all  unite  to  make  up  one  whole.  These 
collections  of  various  ideas,  thus  co-existing  in  the  same 
common  subject,  and  held  together. by  some  unknown 
bond  of  union,  have  been  distinguished  by  the  name  of . 
substances,  a  word  which  implies  their  subsisting  of 
themselves,  without  dependence  (at  least  as  far  as  our 
knowledge  reaches)  on  any  other  created  beings.  Such 
are  the  ideas  we  have  of  gold,  iron,  water,  a  man,  Sec. 
For  if  we  fix  upon  any  one  of  these,  for  instance,  gold, 
the  notion  under  which  we  represent  it  to  ourselves  is 
that  of  a  body  yellow,  very  weighty,  hard*  fusible,  mal- 
leable, &c.  where  we  may  observe,  that  the  several  pro- 
perties that  go  to^the  composition  of  gold,  are  repre- 
sented to  us  by  clear  and  evident  perceptions  ;  the 
union  too  of  these  properties,  and  their  thereby  consti- 
tuting a  distinct  species  of  body,  is  clearly  apprehends 


22  DUNCAN'S  ELEMENTS 

ed  by  the  mind  :  but  when  we  would  push  our  enqui- 
ries farther,  and  know  wherein  this  union  consists, 
what  holds  the  properties  together,  and  gives  them 
their  self-subsistence,  here  we  find  ourselves  at  a  loss. 
However,  as  we  cannot  conceive  qualities,  without  at 
the  same  time  supposing  some  subject  in  which  they 
adhere,  hence  we  are  naturally  led  tc  form  the  notion 
of  a  support,  which,  serving-  as  a  foundation  for  the  co- 
existence and  union  of  the  different  properties  of  things, 
gives  them  that  separate,  and  independent  existence 
under  which  they  are  represented  to  our  conception. 
This  support  we  denote  by  the  name,  substance;  and  as 
it  is  an  idea  applicable  to  all  the  different  combinations 
of  qualities  that  exist  any  where  by  themselves,  they  are 
accordingly  all  called  substances.  Thus  a  house,  a  bow!| 
a  stone,  kc.  having  each  their -distinguishing  properties, 
and  being  conceived  to  exist  independent  one  of  ano- 
ther, the  idea  of  substance  belongs  alike  to  them  all. 

Sec.  II....7Yzs   Division  of  Modes  into  Essential  and 

Accident  ah 
•  In  substances  ^therefore  there  are  two  things  to  be 
considered  :  .first,  the  general  notion  of  self-subsist- 
ence, which,  as  2  have  said,  belongs  equally  to  them  all  ; 
and  then  the  several  qualities,  or  properties,  by  which 
the  different  kinds  and  individuals  are  distinguished 
one  from  another.  These  qualities  are  otherwise  cal- 
Jed  modes,  and  have  been  distinguished  into  essential 
and    accidental,  according  as  they  are  perceived  to  be 

I  separable,  or  inseparable  from  the  subject  to  which  they 

!  belong.  Extension  and  solidity  are  essential  modes  of 
a  stone  ;  because  it  cannot  be  conceived  without  them  ; 
but  roundness  is  only  an  accidental  mode  ;   as  a  stone 

I  may  exist  under  any  shape  or  figure,' and  yet  still  re- 

I    tain  its  nature  and  other  properties. 

j   Sec.  III....77it*  Notion  of  Self-Subsistence   inseparable 

from  Substances. 

I  might  run  farther  into  these  divisions  and  subdivi- 

\   s-ions,   in  which  logicians  have  been  very  fertile  ;    but 

as   they  tend  little  to  the  advancement  of   real  know- 

t  ledge,  and  serve  rather  to  fill  the  .memory  with  words. 


OF  LOGIC.  23 

and  their  significations,  than  furnish  clear  amd  distinct 
apprehensions  of  things,  1  -hall  nojt  trouble  the  reader 
with  them,      It  is  more   material  to  observe,  that   the 
change  of  properties  in  any  substance,  iho'  it  oft-times 
changes  the  nature  of  that  substance,  that  is,  its  spe- 
cies or  kind  ;   yet  it  never  destroys  the  general  notion 
of  self-existence,  but  leaves  that  equally  clear  and  ap- 
plicable, as  before  any  such  alteration  happened.  Wood, 
by  tfeft  application  of  fire  is  turned  into  charcoal  ;  but 
charcoal,    however  different   from  "wood   is  still -.a  sub- 
stance.      In  like  manner,   wax  may  be  converted    into 
flame  arid  smoke  ;    a  human    body   will    moulder   into 
dust  :   yet  these  alterations  destroy  not  their  being  or  - 
existence  ;'  they  are  still  substances  as  before,  tho'  un- 
der a  different  form  and  appearance.    In  the  several  ex- 
periments made    by    chemits,   bodies   undergo   many 
'changes,  and  put  on  successivelv  a  great  variety  of  dif- 
ferent shapes,  and  yet,  by  the  skill  and  address  of  the 
operator,  they  are  often  brought    back    to    their  first 
and  primitive  form.     \Vhat  alteration  can  we  suppose 
the  fire,  or  the  application  of  any  other  body,  to  make, 
unless  on  the  configuration,  texture,  or  cohesion  of  the 
minute  parts  ?  when  these   are  changed,    the   body  is 
proportionably  changed  ;   when   they  return    to   then 
original  state,  the  body  likewise  puts  on  its  first  and 
natural  appearance. 

Sec*  IV....'Founda!!o  i  of  the  different  Species  of  Corpo- 
real Substances. 

All  that  is  essential  to  matter^  therefore,  is  the  cohe- 
sion of  solid  extended  parts  :  but  as  these  parts  are  ca- 
pable of  innumerable  configurations — as  their  texture 
may  be  very  various,  and  the  internal  constitution 
thence  arising  be  of  consequence  extremely  different  in 
different  bodies — we  may  from  these  considerations 
conceive  pretty  clearly  the  source  and  foundation  of  all 
the  different  species  of  corporeal  substances.  Nor  is 
this  a  notion  taken  up  at  random,  or  one  of  those  chi- 
merical fancies  in  philosophy,  derived  rather  from  a 
warmth  and  liveliness  of  imagination,  than  observa- 
tions drawn  from  things  themselves.     Do  we  not  daily 


24  DUNCAN'S  ELEMENTS 

see  our  food,  by  the  changes  it-undergoes  in  the  differ- 
ent avenues  of  the  body,  converted  first  into  blood,  and 
thence  employed  in  nourishing,  building  up,  and  ..en* 
larging,  the  several  parts  of  that  wonderful  fabric  ? 
Rain,  descending  from  the  clouds,  and  mixing  with  the 
mold  or  earth  of  a  garden,  becomes  aliment  for  trees  of 
various  kinds,  puts  on  a  diversity  of  forms,  according  to 
the  different  channels  and  conveyances  through  which 
it  passes  ;  and  at  last,,  after  innumerable  changes  and 
transmutations,  sprouts  forth  in  leaves,  opens  in  budsj 
or  is  converted  into  the  substance  of  the  tree  itself. 
Can  we  conceive  any  greater  difference  between  the 
component  parts  of  gold,  and  those  of  stone,  than  be- 
tween the  moistened  particles  of  garden  mold,  and  those 
new  forms  and  figures  under  which  they  appear,  after 
they  have  been  thus  fashioned  by  nature  for  the  pur- 
poses of  growth  and  nourishment  ? 

Sec.   Vm»Essence  of  Substances  nothing  but  the  inter* 
nal  structure  end  constitution  ; 

If  this  be  duly  attended  to,  it  will  not  appear  won- 
derful to  assert,  that  the  variety  of  material  substances 
arises  wholly  from  the  different  configuration,  size,  tex- 
ture, and  motion  of  the  minute  parts.  As  these  happen 
■to.be  variously  combined,  and  knit  together,  under  dif- 
ferent forms,  bodies  put  on  a  diversity  of  appearances, 
and  convey  into  the  mind  by  the  senses  all  those  sever- 
al impressions,  by  which  they  are  distinguished  one 
from  another.  This  internal  constitution  or  structure 
of  parts  from  which  the  several  properties  that  dis- 
tinguish any  substance  flow,  is  caflcd  the  essence  of 
that  substance,  and  is,  in  fact,  unknown  to  us,  any 
farther,  than  by  the  perceivable  impressions  it  makes 
upon  the  organs  of  sense.  Gold,  as,  has  been  said,  is  a 
body  yellow,  vtry  weighty,  hard,  fusible,  malleable, 
&.C.  That  inward  structure,  and  conformation  ftf  its 
minute  particles,  by  which  they  are  so  closely  linked 
together,  and  irom  which  the  properties  above  men- 
tioned are  conceived  to  flow,  is  called  its  essence  ;  and 
the  properties  themselves. are  the  perceivable  marks  that 
make  it  known  to  us;  and  distinguish  it  from  all  o';her 


OF  LOGIC.  25 

substances  ;  for  our  senses  are  not  acute  enough  to 
reach  its  inward  texture  and  constitution.  The  parts 
themselves,  as  well  as  their  arrangement,  lie  far  be- 
yond the  utmost  penetration  of  human  sight,  even 
when  assisted  by  microscopes,  and  all  the  other  con- 
trivances of  art. 

£ec.   VI Is  wholly  unknown  to  us  end  serves  to  dis- 
tinguish the  Species  ; 

Thus,  as  to  the  essence  or  internal  constitution  of 
gold,  we  are  wholly  in  the  dark  ;  but  many  of  the  pro- 
perties deriyed  from  this  essence,  make  obvious  and. 
distinct  impressions,  as  the  weight,  hardness,  and  yel- 
low colour,  Sec.  These  properties  combined  together, 
and  conceived  as  co-existing  in  the  same  common  sub- 
ject, make  up  our  complex  idea  of  gold.  The  same 
may  be  said  of  all  the  other  species  of  corporeal  sub- 
stances, as  lead,  glass,  water,  &c.  our  ideas  of  them 
being  nothing  else  but  a  collection  of  the  ordinary  qua- 
lities observed  in  them. 

Sec.      VII....7"<?Z  it  is  rightly  presumed  to  be  distinct 
in  all  the  several  kinds. 

This,  hawever,  ought  to  be  observed,  that  though 
the  essence  or  inward  structure  of  bodies  is  altogether 
unknown  to  us,  yet  we  rightly  judge,  that  in  all  the 
several  species,  the  essences  are  distinct.  For  each  spe- 
cies being  a  collection  of  properties,  which,  taken  to- 
gether, are  different  from  thooe  of  every  other  species, 
the  conformation  of  par£s,  on  which  these  properties 
depend,  must  in  like  manner  be  different  ;  and  this,  as 
we  have  said,  constitutes  the  essence.  Iron  and  glass 
are  evidently  distinct  kinds  of  body  ;  their  perceivable 
qualities  have  little  or  nothing  common  ;  and  there- 
fore the  inward  structure  or  constitution  from  which 
these  qualities  flow,  cannot  be  the  same  in  both.  But 
after  all,  this  is  the  only  thing  we  can  with  certainty 
affirm  concerning  these  essences,  which  lying  so  wholly 
in  the  dark,  we  shall  do  well  to  lay  them  aside  in  our 
reasonings  about  things,  and  adhere  to  those  more  in- 
telligible and  settled  ideas  acquired  by  joining  toge- 
ther their  various  properties  and  powers.  For  thus 
jonly  is  true  knowledge  promoted,  when  we  argue  from 
C 


26  DUNCAN'S  ELEMENTS 

known  qualities,  and  not  from  a  supposed  internal  con-^ 
stitution,  which,  however  real  in  itself,  yet  comes  not 
within  the  reach  of  our  faculties,  and  therefore  can 
n$ver  be  a  ground  to  us  for  any  discoveries  or  im- 
provements. 

Sec,  VIII.. ..By  what  steps  we  arrive  at  the  Notions 
of  Immaterial  Substances  ; 
Material  substance,  as  I  have  said,  includes  the  idea 
of  solid,  cohering,  extended  parts,  and  is  divided  into 
different  classes  according  to  the  different^  impressions 
made  upon  the  organs  of  sense.  But,  besides  these 
sensible  ideas  received  from  without,  we  also  experience 
in  ourselves  thinking  and  volition.  These  actions  have 
no  connection  with  the  known  properties  of  body;  nay, 
they  seem  plainly  inconsistent  with  some  of  its  most 
essential  qualities.  For  the  mind  not  only  discovers 
no  relation  between  thinking,  and  the  motion  or  ar- 
rangement of  parts  ;  but  it  also  perceives,  that  consci- 
ousness, a  simple  individual  act,  can  never  proceed  from 
a  compounded  substance,  capable  of  being  divided  in- 
to many.  Let  us  suppose,  for  instance,  a  system  of 
matter  endowed  with  thought  ;  then  either  all  the 
parts,  of  which  this  system  is  composed,  must  think, 
which  would  make  it  not  one,  but  a  multitude  of  dis- 
tinct conscious  beings  ;  or  its  power  of  thinking  must 
arise  from  the  connection  of  the  parts  one  with  another, 
their  motion  and  disposition,  Sec,  which,  all  taken  to- 
gether, contribute  to  the  production  of  thought.  But 
it  is  evident,  that  the  motion  of  parts,  and  manner  of 
combining  them,  can  produce  nothing  but  an  artful 
structure,  and  various  modes  of  motion.  All  machines 
of  human  composition,  as  watches,  clocks,  Sec.  howe- 
ver artfully  their  parts  are  set  together,  however  com- 
plicated their  structure— -though  we  conceive  innume- 
rable different  motions,  variously  conjoined,  and  run- 
ning one  into  another  with  an  endless  diversity,  yet 
never  produce  any  thing  but  figure  and  motion.  If  a 
clock  tells  the  hour  and  minute  of  the  day,  it  is  only 
by  the  motion  of  the  different  hands,  pointing  succes- 
sively at  the  figures  marked  on  the  hour-plate  for  that 
purpose,     We  never  imagine  this  to  be  the  effect    of 


OF  LOGIC.  2? 

thought  or  intelligence  ;  nor  conceive  :t  possible,  by 
any*  refinement  of  structure,  so  to  improve  the  compo- 
sition, as  that  it  shall  become  capable  of  knowledge  and 
consciousness.  The  reason  is  plain  :  thought  is  some- 
thing altogether  different  from  motion  and  figure  ;  - 
there  is  not  the  least  connection  between  them  ;  and 
therefore  it  can  never  be  supposed  to  result  from  them* 
Sec.  IX....^A/c/t  we  otherwise  call  Spirits* 

This  then  being  evident,  that  intelligence  cannot 
arise  from  an  union  or  combination  of  unintelligible 
parts  ;  if  we  suppose  it  to  belong  to  any  system  of  mat- 
ter, we  must  necessarily  attribute  it  to  all  the  parts, 
of  which  that  system  is  composed  ;  whereby,  instead  of 
one,  we  shall,  as  was  before  observed,  have  a  multi* 
tude  of  distinct  conscious  beings.  And  because  mat* 
ter,  how  far  soever  we  pursue  the  minuteness  of  its 
parts,  is  still  capable  of  repeated  divisions,  even  to  in* 
inky  ;  it  is  plain,  that  this  absurdity  will  follow  us, 
through  all  the  suppositions  that  make  thought  inhe* 
rent  in  a  material  substance.  Finding,  therefore,  con* 
sciousness  incompatible  with  the  cohesion  of  solid  se* 
parable  parts  we  are  necessarily  led  to  place  it  in  some 
other  substance,  of  a  distinct  nature  and  properties, 
which  we  call  spirit. 

Sec.   X..,.Body  and  Spirit  distinct  Substances. 

And  here  it  is  carefully  to  be  observed,  that  the  se- 
veral species  of  corporeal  substances,  though  distin- 
guished one  from  another,  and  ranked  under  different 
names  ;  yet,  agreeing  in  some  common  properties, 
which,  taken  together,  make  up  the  notion  of  body, 
are  thence  all  conceived  to  partake  of  this  general  na- 
ture, and  to  differ  only  as  different  modifications  of 
the  same  substance.  Whatever  consists  of  solid  ex- 
tended parts,  is  called  matter  ;  and  as  all  the  various 
specie-s  of  body,  however  distinguished  from  one  ano- 
ther by  their  several  properties,  have  yet  this  in  com- 
mon, that  they  are  made  up  of  such  solid  separable 
parts,  hence  they  fall  naturally  under  the  general  de- 
nomination of  material  beings,  and  are  not  conceived 
to  differ,  but  in  their  form.  1  bus  gold,  antimony,- wood,. 
&c.  alike  partake  of  the  notion  of  body  $  they  are  aH 


28  DUNCAN'S  ELEMENTS 

equally  material  substances,  and  have  no  other  differ* 
ence,  but  what  arises  from  the  different  structure  and 
conformation,  Sec.  of  parts,  as  we  have  shewn  above. 
But  spirit  is  something  altogether  distinct  from  body, 
nay,  and  commonly  placed  in  opposition  to  it  ;  for 
-which  reason,  the  beings  of  this  class  are  called  imma- 
terial ;  a  word  that  implies  not  any  thing  of  their  na- 
ture, but  merely  denotes  its  contrariety  to  that  of  matter. 
Sec.   XI.    Thtrt  may  be  many  various  Species  of  Sub  - 

stances,  besides  those  that  come  within  the  reach   of 

our  Faculties, 

Body  and  spirit,  therefore,  differ  not  as  species  of  the 
same  substance,  but  ar.e  really  distinct  kinds  of  sub- 
stances, and  serve  as  general  heads  under  which  to 
rank  all  the  particular  beings  that  fall  within  the  com- 
pass of  our  knowledge.  For  we  having  no  ways  of  per- 
ception but  sense  and  consciousness,  can  have  no  no- 
tices of  things,  but  as  derived  from  these  two  inlets. 
By  our  senses  we  are  informed  of  the  existence  of  so- 
lid extended  substances  ;  and  reflection  tells  us,  that 
there  are  thinking  conscious  ones.  Beyond  these  our 
conceptions  reach  not  ;  and  therefore,  though  there  may 
be  many  other  kinds,  as  different  from  them  as  they  are 
from  cne  another,  yet  having  no  faculties  suited  to 
them,  they  are  as  remote  from  our  knowledge,  as  light 
and  colours  from  the  apprehension  of  a  man  born  blind. 
Ibelievexit  will  hardly  be  doubted  but  the  substance 
of  the  Creator  differs  more  from  that  of  his  creatures, 
than  any  two  created  substances  can  from  one  ano- 
ther ;  and  therefore  when  we  call  God  a  spirit,  wc 
ought  not  rashly  to  presume,  that  he  is  so  in  the  same 
sense  in  which  the  human  soul  is  a  spirit.  The  word 
is,  indeed,  used  by  us,  to  denote  in  general  all  thinking 
intelligent  substances,  in  which  sense  God  is  very  fitly 
called  a  spirit.  But  it  were  the  height  of  folly  to  ima- 
gine, because  this  name  is  applied  as  well  to  the  mind 
of  man  as  the  Creator,  that  therefore  they  partake  of 
one  common  nature,  and  differ  only  as  different  modi- 
fications of  the  same  substances  This  I  mention  here, 
to  check  the  presumption  of  the  human  mind,  always 
forward  to  conclude,    that  every  thing  cornea  withim 


OF  LOGIC.  29 

Its  reach,  and  to  deny  existence  to  whatever  exceeds 
the  comprehension  of  its  scanty  and  limited  powers. 
Beings  of  a  superior  class  may  enjoy  many  ways  of  per- 
fection unknown  to  us,  from  which  they  receive  no- 
tices as  diffe  ent  from  those  in  our  minds,  as  the  ideas 
we  apply  to  pirit  are  from  the  ideas  we  apply  to  body* 
Solid  and  thinking  beings  are,  it  is  true,  the  only  ideas 
of  substance  that  we  are  able  to  frame  ;  but  this  is  no 
more  an  argument  against  the  existence  of  other  kinds, 
than  the  want  of  the  ideas  of  light  and  colours  in  a 
blind  man  would  be  a  good  argument  against  the  reali- 
ty or  possibility  of  such  perceptions. 
See,  XII. ...Difference  in  the  manner  of  conceiving 
Corporeal  and  Spiritual  Substances*  - 
Before  I  dismiss  this  subject,  it  may  not  be  improper 
to  take  notice  of  a  remarkable  difference  as  to  the  man- 
ner of  our  conceiving  corporeal  and  spiritual  substan- 
ces. Those  of  the  first  kind  convey  themselves  into 
the  mind  by  impressions  made  upon  the  organs  of  sense  ; 
and  as  these  impressions  are  different  in  different  bodies, 
the  ideas  they  produce  must^of  course  vary  in  propor- 
tion. Thus  we  get  preceptions  of  distinct  powers  and 
properties,  and  range  bodies  into  classes,  according  as 
we  find  them  to  agree  or  disagree  in  these  their  obser- 
vable qualities.  But  it  is  not  so  in  our  notion  of  spi- 
rits ;  for  having  no  conception  of  their  powers  and 
operations  but  by  what  we  feel  and  experience  within 
ourselves,  we  camiot  ascribe  to  them  properties  or  ways 
-  of  knowledge,  distinct  from  those  suggested  to  us  by 
our  own  consciousness.  And  hence  it  is,  that  though 
we  readily  own  there  may  be  ^various  ranks  of  spiritual 
beings,  yet  we  are  not  to  imagine  them  divided  from 
one  another  by  any  diversity  of  powers  and  operations, 
but  merely  by  possessing  the  same  powers,  &c.  in  a 
higher  orlower  degree.  It  is  not,  however,  repugnant 
to  reason,  that  they  should  be  distinguished  by  their  se- 
veral properties  in  like  manner  as  sensible  things  are 
by  the  different  qualities  observable  in  them  ;  but  pro- 
perties of  intellectual  natures,  distinct  from  those  of  our 
own  minds,  being  altogether  remote  from  our  concep- 
tion, cannot  serve  as  a  means  whereby  to  distinguish 
C  % 


30  DUNCAN'S  ELEMENTS 

their  different  orders.  We  are,  therefore,  necessitated 
to  conceive  of  them  in  a  manner  suited  to  our  way  of 
knowledge  ;  and  when  we  would  rank  them  into  spe- 
cies, according  to  the  degrees  of  superiority  they  are? 
imagined  to  possess  in  the  scale  of  being,  we  ascribe  to 
them  what  we  find  most  excellent  in  ourselves,  as  know- 
ledge, thinking,  foresight,  &c.  and  those  in  different 
measures  proportioned  to  the  station  peculiar  te  each 
rank  or  species.  But  that  this  is  a  very  imperfect  way 
of  distinguishing  the  various  orders  of  intellectual  be* 
ings,  will  not,  I  think,  need  many  words  to  make  it  ap- 
pear ;  especially  if  we  consider,  that  the  manner  of 
communicating  their  thoughts,  without  the  interven- 
tion of  bodily  organs,  is  a  thing  to  us  altogether  in- 
comprehensible, and  necessarily  leads  us  to  suppose, 
that  they  have  ways  of  perception  and  knowledge 
which  our  faculties  cannot. give  us  any  notice  of. 

Sec.  XIII....  The  bounds  of  Knowledge  in  our  present 
state  very  narrow. 
But  I  shall  not  pursue  these  reflexions  farther  ;  what 
Las  been  said  sufficing  to  give  us  some  little  insight  into 
the  extent  and  capacity  of  our  own  minds ;  to  convince 
us  that  our  present  state  will  not  admit  of  a  perfect  and 
adequate  comprehension  of  things;  and  to  let  us  see, 
that  there  may  be  other  ways  of  knowledge,  beyond  the 
reach  of  the  faculties  we  now  enjoy ;  which  yet,  in  suc- 
ceeding stages  of  our  existence,  we  may  arrive  at,  when, 
being  freed  from  the  present  cumbersome  load  of  the 
body?  we  shall  mount  up  to  stations  of  greater  eminence, 
and  advance  by  a  perpetual  series  of  approaches  towards 
him,  who  is  the  standard  of  perfection  and  happiness. 


Cfmp.  iv. 

OF  IDEAS  FRAMED  BY  THE  MIND. 

Sec.   I..../n  framing  many  complex  Ideas,  the  Mind  is 
wholly  active,  and  proceeds  by  a  voluntary  choice* 

HITHERTO  we  have  considered  only  such  combi- 
nations of  our  simple  ideas  as  have  a  real  union 


OF  LOGIC.  t€ 

in  nature,  and  are  suggested  to  the  mind  by  things  - 
themselves  variously  affecting  our  perception  :  it  is  now*> 
time  to  take  a  view  of  the  other  cias3  of.  our  complex 
notions  ;  I  mean  those  arbitrary  collections  of  different 
ideas,  which  we  on  many  occasions  bring  together  by 
that  power  which  we  fifid  in  ourselves,  of  uniting,  com- 
paring, and  diversifying  our  notices  of  things.  In  the 
reception  of  simple  ideas,  and  even  in  those  of  substan- 
ces, the  understanding  is  wholly  passive,  and  the  per- 
ception* produced  correspond  to  the  impressions  made 
upon  it.  When  we  see  a  house,  or  a  tree,  they  neces- 
sarily appear  each  under  its  proper  form;  nor  is  it  in 
our  power  to  receive  from  these  objects  other  ideas  than 
what  they  are  fitted  to  produce.  But  in  this  second 
class  of  complex  conceptions,  the  mind  acts  voluntari- 
ly and  of  choice  ;  it  combines  only  such  ideas  as  are 
supposed  best  to  suit  its  present  purpose;  and  alters  or 
changes-  these  combinations,  by  inserting  some,  and 
throwing  out  others,  according  as  the  circumstances  of' 
things  require  their  being  viewed  in  different  lights. 
Now  as  this  is  by  far  the  most  comprehensive  branch  of 
our  ideas,  and  includes  those  that  most  frequently  occur 
in  the  search  and  pursuit  of  knowledge,  I  shall  endea- 
vour to  treat  them  in  the  exactest  order  and  method; 
and  for  that  purpose  range  them  under  several  heads, 
according  to  the  different  acts  of  the  mind  exerted  in 
framing  and  putting  them  together. 

Sec.  II....  Three  several  Acts  exerted  by  the  Mind  in 
framing  its  arbitrary  Ideas,  viz.   Composition  ; 

These  acts  may  in  the  general  all  be  reduced  to  three* 
1,  Composition,  when  we  join  many  simple  ideas  toge- 
ther, and  consider  them  as  one  picture  or  representa- 
tion. Such  are  our  ideas  of  beauty,  gratitude,  a  fur- 
long, Sic.  And  here  let  it  be  observed,  that  the  mind 
sometimes  confines  itself  to  the  various  consideration  of 
the  same  idea,  and,  by  enlarging  it  in  different  degrees, 
,  exhibits  it  under  a  diversity  of  forms.  Thus  by  adding 
units  together,  in  distinct  separate  collections,  we 
come  by  the  several  combinations  of  numbers,  as  a 
dozen>  a  score,  a  million.      At  other  times  we  unite 


9*  DUNCAN'S  ELEMENTS 

perceptions  of  different  kinds;  in  which  case  the  com- 
position is  more  manifest,  and  the  idea  itself  becomes  of 
course  more  complicated.  Harmony,  for  instance,  is  a 
compound  .idea,  made  up  of  many  different  sounds 
united;  all  which  the  musician  must  have,  and  put  to- 
gether in  his  mindjjbefore  the  ear  can  be  entertained 
■with  the  actual  performance.  Now  although  the  act  of 
the  mind  is  in  some  measure  exerted  in  the  framing  of 
all  our  complex  notions,  yet  as  many  of  them  include 
certain  limited  and  particular  considerations,  arising 
from  other  operations  of  the  mind  employed  about 
them,  it  is  necessary  to  take  account  of  these  acts  also, 
if  we  would  conceive  clearly  the  manner  in  which  the 
*everal  species  of  our  compound  ideas  are  formed. 
Sec.   \\1..*. Abstraction* 

2.  The  next  operation  therefore  of, the  mind,  about  its 
ideas,  is  abstraction,  when  we  separate  from  any  of  our 
conceptions  all  those  circumstances  that  render  it  parti- 
cular, or  the  representative  of  a  single  determinate 
object ;  by  which  means,  instead  of  standing  for  an  in- 
dividual, it  is  made"  to  denote  a  whole  rank  or  class  of 
things.  Thus  upon  seeing,  for  instance,  a  square  or 
circle,  we  leave  out  the  consideration  of  their  bulk, 
and  everything  else  peculiar  to  them,  as  they  imme- 
diately affect  our  sight,  retaining  only  the  notion  of 
their  figure  and  shape.  In  this  manner  we  get  our^-e- 
nerat  ideas  ;  for  such  naked  '  appearances,  separated 
from  the  circumstances  of  time  place,  &c.  serve  the 
mind  as  standards  by  which  to  rank  and  denominate 
particular  objects.  When  therefore  me  meet  with  a 
figure  answering  to  that  shape  and  form  we  had  laid 
up  in  oui\understandings,  Itis  immediately  referred  by 
the  mind  to  this  pattern,  and  called  by  its  name, 
■which  by  this  means  becomes  proper  to  the  whole 
species.  Thus  a  square,  or  circle,  are  universal  terms, 
common  to  all  figures  of  that  particular  shape,,  and 
alike  applicable  to  them  wherever  they  exist  ;  in  like 
manner  as  the  ideas  themselves  are  general,  and  repre- 
sentatives of  all  the  kind.  £ 
Sec.  TV..,.And  Comparison, 

3«  The  third  and  last  act  of  the  mind  about  its  ideas', 


_GF  LOGIC.  38 

is  the  comparing  them  one  with  another,  when  we  carry 
our  consideration  of  things  beyond  the  objects  them- 
selves, and  examine  their  respects  and  correspondences 
in  reference  to  other  things  which  the  mind  brings 
into  view  at  the  same  time.  It  is  thus  we  get  all  our 
ideas  of  relations,  as  of  greater,  less,  older,  younger, 
father,  son,  and  innumerable  others.  This  threefold 
view  of  our  ideas,  as  either  compounded  of  many  others 
put  together,  or  made  universal  by  the  abstraction  of 
the  mind,  or  as  representing  the  various  relations  and 
habitudes  of  things,  will  give  us  an  opportunity  of  ob- 
serving whatever  is  most  curious  and  useful  in  this 
fundamental  branch  of  knowledge,  and  of  explaining 
the  manner  and  procedure  of  the  understanding  in  en- 
larging its  views,  and  multiplying  the  objects  of  per- 
ception. That  we  may  therefore  conceive  of  this 
matter  with  the  greater  order  and  clearness,  we  shall 
make  each  of  these  several  ideas  the  subject  of  a  dis- 
tinct article. 


ART.  I. 


OF  COMPOUND  IDEAS. 

Sec.  I. •••Compound   Ideas  considered  here   merely  etg 
Combinations  of  the  Understanding, 

WE  begin  therefore  with  those  ideas  which  maf 
be  properly  termed  compound,  as  being  derived 
from  that  power  the  mind  has  of  uniting  many  concep-v 
tions  into  one.  Though  this  class  comprehends,  in  some 
sort,  all  our  complex  notions,  yet  they  are  at  present 
considered  merely  as  they  are  combinations  of  the  un- 
derstanding, and  with  a  view  to  those  particular  ideas 
out  of  which  they  are  framed.  Here,  as  was  already- 
observed,  the  mind  sometimes  proceeds  by  enlarging 
and  diversifying  the  same  idea  ;  at  other  times  it  brings 
together  ideas  of  different  kinds  ;  and  in  both  ways 
finds  infinite  scope  and  variety.  But  that  we  may  fol- 
low the  natural  procedure  of  the  intellect,  and  trace  it 
in  its  advances  from  simple  to  more  complicated  acts> 
Hf«  shall  first  take  a  view  of  it  as  employed  about  ©*• 


34  DUNCAN'S  ELEMENTS 

and  the  same  idea,  where  perhaps  we  may  m«et  witk 
such  instances  of  address,  management,  and  contri- 
vance, as  will  appear  perfectly  astonishing  to  one  who 
has-never  set  himself  seriously  to  consider  the  manner 
and  conduct  tff  his  own  mind. 

Sec.  Il„. .Unity  the  Original  and  Foundation  of  all  our 
Ideas  of  Number* 
The  most  obvious  and  simple  idea  we  have,  is  that  of 
Unity  or  one.  By  adding  it  to  itself  continually,  and 
retaining  the  several  collections  in  our  minds,  we  come 
by  all  the  different  combinations  of  numbers,  in  which 
we  readily  perceive  an  endless  diversity.  All  these 
ideas  are  nevertheless  evidently  distinct  among  them- 
selves, the  addition  of  a  single  unit  constituting  a 
number  a§  clearly  different  from  that  immediately  be- 
fore it-,  as  any  two  the  most  remote  ideas  are  from  one 
ano/cher.  But  that  the  understanding  may  not  lose  it- 
self in  the  consideration  of  those  infinite  combinations 
of  which  unity  is  capable,  it  proceeds  by  regular  steps  ; 
and  beginning  with  the. original  idea  itself,  pursues  it 
through  all  its  varieties,  as  they  are  formed  by  the  re- 
peated continual  addition  of  unit  after  unit.  Thus 
numbers,  a  re  made  to  follow  one  another  in  an  orderly 
progression,  and  the  several  successive  collections  are 
distinguished  by  particular  names. 

Sec.  III....77i<?  artful  composition  of  the  names  of 

Numbers  a  great  help  to  our  conceptions  ; 
And  here  we  may  take  notice  cf  a  wonderful  artifice 
made  use  of  by  the. mind,  to  facilitate  and  help  it  for- 
ward in  its  conceptions.  For  as  the  advance  from  num- 
ber to  number  is  endless,  were  they  all  to  be  distinguish- 
ed by  different  denominations  that  had  no  connexion  or 
dependence  one  upon  another,  the  multitude  of  them, 
must, soon  overcharge  the  memory,  and  render  it  impos- 
sible for  us  to  go  any  great  way  in  the  progress  of  num- 
bering. For  this  reason  it  is  so  contrived,  that  the 
change  of  names  is  restrained  to  a  few  of  the  first  com- 
binations, all  the  rest  that  follow  being  marked  by  a 
repetition  of  the  same  terms,  variously  compounded  and 
linked  together.  Thus  thirteen  is  ten  and  three,  four- 


OF  LOGIC.  35 

teen,  ten  and  four,  and  so  on  to  twenty,  or  two  tens, 
when  we  begin  again  with  one,  two,~&cc.  until  we  ad- 
vance to  thirty,  or  three  tens.  In  this  manner  the 
progression  continues !  and  when  we  arrive  at  ten  tens, 
■to  prevent  confusion  by  a  two  frequent  repetition  of 
the  same  word,  that  sum  is  distinguished  by  the  name 
of  a  hundred.  Again,  ten  hundred  is  called  a  thousand, 
at  which  period  the  computation  begins  anew,  running 
through  all  the  former  combinations,  as  ten  thousand, 
a  hundred  thousand,  ten  hundred  thousand  ;  which  last 
collection,  for  the  reasons  mentioned  above,  has  the 
name  of  a  million  appropriated  to  it.  With  this  mil- 
lion, we  can  begin  as  before,  until  it  is  repeated  a  mil- 
lion of  times ;  when,  if  we  change  the  denomination 
to  billions,  and  advance  in  the  same  manner  through 
trillions,  quartillians,  the  series  may  be  carried  on  with- 
out confusion,  to  any  length  wc  please. 

Sec.  IV.. ..And  of  the  principal  Reasons  that  our  Ideas 
of  Numbers  are  so  remarkably  distinct. 

This  artful  combination  of  names"  to  mark  the  gra- 
dual increase  of  numbers,  is  perhaps  one  of  the  greatest 
refinements  of  the  human  understanding,  and  particu- 
larly deserves  our  admiration  for  the  manner  of  the 
composition  ;  the  several  denominations  being  so  con- 
trived as  to  distinguish  exactly  the  stages  of  the  pro- 
gression, and  point  out  the  distance  from  the  begin- 
ning of  the  series.  By  this  means  it  happens,  that  our 
ideas  of  numbers  are  of  all  others  the  most  accurate 
and  distinct  ;  nor  does  the  multitude  of  units  assem- 
bled together,  in  the  least  puzzle  or  confound  the  un- 
derstanding. It  is  indeed  amazing,  that  the  mind  of 
man,  so  limited  and  narrow  in  its  views,  should  yet 
here  seem  to  shake  off  its  natural  weakness,  and  disco- 
ver a  capacity  of  managing  with  ease  the  most  bulky 
and  formidable  collections.  If  we  enquire  particular- 
ly into  the  reason  of  this,  we  shall  find  it  wholly  owing 
to  the  address  of  the  mind  in  thus  distinguishing  num- 
bers by  different  names,  according  to  the  natural  or- 
der of  progression.  For  as  those  names  are  made  to 
grow  one  ou£  of  another,  they  may  be  aptly  compared 


36  DUNCAN'S  ELEMENTS 

to  a  chain,  all  whose  parts  are  linked  together  by  an 
obvious  and  visible  connexion.  Hence  it  comes  to  pass, 
that  when  we  fix  our  thoughts  upon  any  number,  how- 
ever great  and  seemingly  unmanageable ;  yet,  if  it  is 
once  determined  to  a  particular  name,  we  find  it  easy 
to  run  back  through  all  the  stages  of  the  progression, 
even  till  we  arrive  at  unity  itself.  By  this  means  we 
see,  with  a  single  glance  of  our  minds,  not  only  the  two 
extremes  of  the  number  under  consideration,  but  also 
the  several  intermediate  parts,  as  they  are  united  to 
make  up  the  whole. 

Sec  V.t..^  they  kelp  us  to  a  clear  Perception  of  the  in* 
terjacent  Parts. 

Now  it  is  to  this  clear  and  accurate  view  of  the  in- 
terjacent ideas,  that  we  owe  our  so  distinct  perception 
of  the  various  combinations  of  numbers.  And  indeed  we 
may  observe,  in  the  general,  that  all  our  ideas  of  quan- 
tity, especially  when  they  grow  to  be  very  large,  are 
no  otherwise  ascertained  than  by  that  perception  we 
have  of  the  intervening  parts,  lying,  if  I  may  so  say, 
between  the  extremes.  When  we  look  at  any  object 
Considerably  distant  from  us,  if  we  have  a  clear  view 
of  the  interjacent  lands  anH  houses,  we  are  able  to  de- 
termine pretty  nearly  of  its  remoteness  ;  but  if,  with- 
out such  a  knowledge  of  the  intervening  spaces,  we 
should  pretend  to  judge  of  the  distance  of  objects,  as 
when  we  see  the  spire  of  a  steeple  behind  a  wall,  or  be- 
yond a  mountain,  every  one's  experience  is  a  proof  how 
liable  we  are,  in  these  cases,  to  be  deceived.  Just  so  it 
is  in  judging  of  duration.  When  we  carry  back  our 
thoughts  to  any  past  period  of  our  lives,  without  con- 
sideration of  the  number  of  years  or  months,  we  find 
that  our  idea  of  the  time  elapsed  grows  more  distinct, 
in  proportion  as  we  become  sensible  of  the  intermedi- 
ate parts  of  our  existence.  At  first  we  are  apt  to  judge 
the  distance  extremely  short;  but  when  we  set  our- 
selves to  consider  our  several  successive  thoughts  and 
actions,  the  idea  of  the  duration  grows  upon  us,  and 
continues  to  increase  as  the  attention  of  the  mind  bring* 
new  periods  of  life  into  view. 


OF  LOGIC.  zr 

Sec.  VI.,*JVithout  names,  nue  cannot  make  any  pro* 
gress  in  Numbering* 

Hence  it  will  be  easy  to  conceive  how  much  the  mini 
is  helped  forward  in  its  perception  of  number,  by  that 
ready  comprehension  of  all  the  several'stages  in  a  pro- 
gression. Which  peculiarly  belongs  to  ideas  of  this  class. 
But  this,  as  I  have  before  intimated,  we  derive  from  the 
orderly  series  and  connexion  of  names,  insomuch  that 
where  they  cease,  the  computation  of  numbers  also  ceases 
with  them.  We  can  have  no  idea  of  any  sum,  without 
a  knowledge  of  all.  the  terms  that  go  before,  according 
to  the  natural  order  in  which  they  follow  one  another  ; 
so  that  he  who  cannot,  in  a  regular  way,  count  to  nine- 
ty-nine, will  never,  while  that  incapacity  continues,  be 
able  to  form  the  idea  of  a  hundred;  because  the  chain 
that  holds  the  parts  together,  is  to  him  wholly  unser- 
viceable, nor  can  he  represent  to  his  mind  the  several 
interjacent  combinations,  without  which  it  is  impossi- 
ble in  this  case  to  arrive  at  a  distinct  perception. 

Sec.  VII....  The  great  advantages  of  Address  in  Class- 
ing our  complex  Conceptions. 
I  have  insisted  the  more  largely  upon  this,  not  only 
because  it  is  by  number  that  we  measure  all  other 
things,  as  duration,  extension,  motion,  &x.  but  also 
because  it  lets  us  into  the  most  natural  view  of  the  con- 
duct and  procedure  of  the  understanding,  and  makes  u$ 
sensible  of  the  great  art  and  address  that  is  necessary  in 
the  classing  our  very  complex  conceptions.  He  that  can 
so  put  together  the  component  parts  of  an  idea,  as  that 
they  shall  lie  obvious  to  the  notice  of  the  mind,  and  pre- 
sent themselves,  when  occasion  requires,  in  a  just  and 
orderly  connexion,  will  not  find  it  very  difficult  to  obtain 
clear  and  accurate  perceptions,  in  most  of  those  sub- 
jects about  which  our  thoughts  are  conversant.  For  the 
great  art  of  knowledge  lies  in  managing  with  skill  the 
capacity  of  the  intellect,  and  contriving  such  helps  as, 
if  they  strengthen  not  its  natural  powers,  may  yet  ex- 
pose them  to  no  unnecessary  fatigue,  by  entangling  and 
perplexing  them  with  considerations  remote  from  the 
business  in  hand*     When  ideas  become  very  complex, 

n 


38  DUNCAN'S  ELEMENTS 

and  by  the  multiplicity  of  their  parts  grow  too  unwieldy 
to  be  dealt  with  in  the  lump,  we  must  ease  the  view  of 
the  mind,  by  taking  them  to  pieces,  and  setting  before 
it  the  several  portions  separately,  one  after  another. 
By  this  leisurely  survey  we  are  enabled  to  take  in  the 
whole ;  and  if  we  can  draw  it  into  such  an  orderly  com- 
bination, as  will  naturally  lead  the  attention,  step  by 
step,  in  any  succeeding  consideration  of  the  same  idea, 
we  shall  ever  have  it  at  command,  and  with  a  single 
glance  of  thought  be  able  to  run  over  all  its  parts.  I 
have  therefore  explained  here,  at  some  length,  the  con- 
duct of  the  mind  in.  numbering;  it  seeming  to  me  the 
best  model  in  this  kind,  whether  we  consider  the  many 
advantages  derived  from  such  an  orderly  disposition  of 
our  ideas,  or  the  great  art  and  skill  displayed  in  binding 
these  ideas  together.  This  also  is  farther  remarkable, 
in  the  consideration  of  number,  that  from  it  chiefly  we 
derive  the  notion  we  have  of  infinity ;  it  being  appar- 
ent, that,  in  adding  number  to  number,  there  is  no 
end  ;  the  possibility  of  doubling  or  increasing  our  stock 
in  any  degree,  remaining  as  obvious  to  the  understand- 
ing, after  a  great  and  continued  run  of  progressions, 
as  when  it  first  began  the  computation. 

Sec.  VIII...,  The  Consideration  of  Number,  of  great  Use 
in  ascertaining  our  Ideas  of  Space  and  Duration, 

If  we  now  turn  our  thoughts  towards  space  and  du- 
ration, here  too  we  shall  find  that  \ve  very  seldom  ar- 
rive at  clear  and  distinct  ideas  of  either,  but  when  we 
introduce  the  consideration  of  number.  The  more  ob- 
vious and  limited  portions,  it  is  true,  easily  slide  into 
the  mind,  in  the  natural  way  of  perception  ;  but  it 
was  the  necessity  of  comparing  these  together,  that 
pu.t  us  upon  the  contrivance  of  certain  stated  measures 
by  which  precisely  to  determine  the  quantity  in  each. 
Thus,  inches,  feet,  yards,  miles,  &c.  ascertain  our  ideas 
of  extension  ;  as  minutes,  hours,  days,  years,  &c.  mea- 
sure the  progress  of  duration.  The  lesser  parts,  as  ly- 
ing most  open  to  the  notice  of  the  understanding,  and 
being  more  on  a  level  with  its  powers,  are  retained. 
yfhk  tolerabk    exactness  j    and   the  larger  portion^ 


OF  LOGIC.  39 

when  the  number  of  repetitions  of  which  they  are 
made  up  is  known,  are  thereby  also  reduced  into  clear 
and  determinate  conceptions.  A  foot,  and  yard,  are 
measures  easily  comprehended  by  the  mind  ;  nor  do  Ave 
find  any  difficulty  in  conceiving  a  mile,  when  we  consi- 
der it  as  equal  to  a  certain  number  of  yards.  If  we  arc 
still  for  increasing  the  standard,  we  may  take  the  se- 
midiameter  of  the  earth,  and  supposing  it  equal  to 
8b00  miles,  make  use  of  it  as  a  measure  by  which  to 
ascertain  the  distance  of  the  sun  or  fixed  stars.  Just  so 
it  is  in  duration  ;  from  hours  we  rise  to  days,  months, 
and  years  ;  by  these,  repeated,  and  added  together, 
we  measure  time  past,  or  can  run  forward  at  pleasure 
into  futurity,  and  that  without  any  confusion  or  per* 
plexity. 

Sec.  lX*...J7ithout  they  are  apt  to  degenerate  into  a 
confused  and  irregular  Heap. 
It  is  however  to  number  alone  that  we  owe  this  dis- 
tinctness of  perception,  inasmuch  as  space  and  time, 
considered  apart  from  the  regular  and  orderly  repeti- 
tion of  miles  or  years,  leave  no  determinate  impres- 
sions in  the  mind,  by  which  to  know  and  distinguish 
their  several  portions.  Ideas  of  either,  thus  taken  in 
tt  a  venture,  are  a  confused  and  irregular  heap,  especi- 
ally where  we  endeavour  to  enlarge  and  magnify  our 
views,  and  give  full  play  to  the  powers  of  our  intel- 
lect. Something  indeed  the  mind  conceives,  vast  and 
mighty,  but  nothing  that  is  precise,  accurate,  and  just. 
But  when  it  begins  to  consider  these  ideas  as  made  up 
cf  parts,  and  fixing  upon  such  as  are  proportioned  to 
its  reach,  sets  itself  to  examine  how  often  they  are  re- 
peated to  make  up  the  whole,  the  perceptions  of  the  un- 
derstanding put  on  a  new  form,  and  discover  their  ex- 
act bounds  and  limits. 

Sec.  %»:J[nfiMtj  an  Object  too  mightj for  the  Survey  of 
,  the  human  Mind, 

And  thus,  as  before  in  number,  so  here  in  extension 
and  duration,  the  mind  begins  with  simple  and  obvious 
notices,  advancing  by  degrees  to  more  enlarged  and 
intricate  conceptions.  A  day,  or  a  furlong,  are  of  easy 


40  DUNCAN'S  ELEMENTS 

apprehension  to  the  understanding,  and  by  their  subdi- 
visions into  still  lesser  spaces,  exhibit  themselves  dis- 
tinctly in  all  their  parts.  With  these  variously  re- 
peated, we  travel  through  space  and  time  ;  so  that  be- 
ing able  to  reduce  all  our  ideas  of  this  class,  however 
mighty  and  enlarged,  to  the  clear  and  determinate  per- 
ceptions of  number,  we  can  conduct  our  thoughts  with- 
out perplexity,  and  never  find  ourselves  puzzled,  but 
when,  presuming  too  much  on  our  own  strength,  we 
launch  into  speculations,  that  stretch  beyond  the  pow- 
ers of  the  human  intellect.  Number  may  be  compared 
to  a  line,  that,  setting  out  from  unity,  runs  on  in  a  con- 
tinued increase  of  length,  without  a  possibility  of  ever 
arriving  at  its  ultimate  period.  So  far  as  we  pursue  it 
in  our  thoughts,  and  trace  its  regular  advances,  so  far 
our  ideas  are  accurate  and  just.  But  when  we  let  loose 
our  understandings,  after  a  boundless  remainder,  and 
would  fathom  the  depth  of  infinity,  "we  find  ourselves 
fpst  amidst  the  greatness  of  our  own  conceptions* 
Some  notions,  it  is  true,  we  have,  but  such  as,  exceed- 
ing the  dimensions  of  the  mind,  lie  involved  in  dark- 
ness and  obscurity  ;  and  being  destitute  of  order,  me- 
thod, and  connexion,  afford  no  foundation  whereon  to 
build  any  just  and  accurate  conclusion. 

Sec.  ~KI...»  Never  represented  in  its  full  Dim  ens  ions  ^but 
bj  an  endless  and  ever  growing  Idea. 

And  this  perhaps  may  be  the  reason  why  many  mo- 
dern philosophers,  in  their  discourses  concerning  infi- 
nity, have  run  into  apparent  contradictions  ;  because, 
encountering  an  object  too  large  for  the  survey  of  the 
understanding,  they  found  themselves  surrounded  with 
inextricable  difficulties,  which  their  scanty  and  defec- 
tive ideas  were  by  no  means  able  to  dissipate  or  remove. 
The  truth  of  it  is,  finite  ideas  alone  are  proportioned 
to  a  finite  understanding  ;  and  although  we  sire  not 
wholly  without  a  notion  of  the  infinity  of  number, 
yet  it  is  not  such  a  one  a3  comprehends  and  exhausts 
its  object,  or  exhibits  it  to  the  mind  in  its  full  size 
and  dimensions.  We  only  see  the  idea,  as  capable  of 
an  endless  increase;  but  cannot  by  any  effort  of  thought 


OF  LOGIC.  41 

take  in  the  whole  prospect  ;  and  indeed  it  is  properly 
that  part  of  it  which  lies  beyond  the  reach  of  our  per- 
ception, and  still  remains  to  be  taken  into  the  account, 
to  which  we  give  the  name  of  infinity. 

Sec.  Xll...»Duration^nvhet?ier  considered  as  pest  or 
to  come,  Boundless,  whence  our  Idea  of  Eternity. 
This  idea  of  the  infinity  of  number,  imperfect  as  it 
may  seem,  is  nevertheless  that  by  which  the  mind  as- 
cends to  the  conception  of  eternity  and  immensity.  For 
when  we  consider  duration,  either  as  past  or  to  come, 
we  find  nothing  to  stop  the  progress  of  our  thoughts, 
in  the  repetition  of  years,  or  millions  of  years  :  the 
farther  we  proceed,  the  more  the  idea  grows  upon  us  ; 
and  when  we  have  wearied  ourselves  with  vain  efforts, 
we  must  own  at  last  that  we  can  no  more  arrive  at  the 
end  of  duration,  than  at  the  end  of  number.  It  is 
true,  .the  several  generations  of  men  rise  and  disappear 
in  very  quick  successions  ;  earth  itself  may  decay  ;  and 
those  bright  luminaries  that  adorn  the  firmament  of 
heaven,  be  extinguished.  But  the  course  of  time  will 
not  be  thereby  disturbed  ;  that  flows  uniform  and  in- 
variable, nor  is  bounded  by  the  period  of  their  exist- 
ence. This  double  view  of  duration,  as  having  already 
revolved  through  numberless  ages,  and  yet  still  ad- 
vancing into  futurity  in  an  endless  progression,  pro- 
perly constitutes  our  ideas  of  eternity.  We  speak  in- 
deed of  an  eternity  past,  an  eternity  to  come,  but 
both  these  are  bounded  at  one  extreme  :  the  former 
terminates  in  the  present  moment,  and  therefore  has  an 
end  :  the  latter  sets  out  from  the  same  period,  and 
therefore  has  a  beginning;  but,  taken  together,  they 
form  a  line  both  ways  infinitely  extended,  and  which 
represents  eternity  in  its  full  dimensions. 

Sec.  XIII. ...  The  Idea  of  Immensity  derived  from  the 
Consideration  of  Space  ever  growing  on  all  side-  of  us. 
As,  in  the  consideration  of  time,  we  fix  upon  the 
present  moment,  regarding  it  as  the  middle  point  which 
divides  the  whole  line  of  duration  into  two  equaj  pa-ts  ; 
so,  in  the  consideration  of  space,  th.u  particuhi.  place 
in  which  we  exist  is  looked  upon  as  a  kind  erf  centre  to 
D  2 


42  DUNCAN'S  ELEMENTS 

the  whole  expansion.  From  thence  we  let  loose  our 
thoughts  on  every  side — above,  below,  around — and  find 
we  can  travel  on,  in  the  repetition  of  miles,  and  mil- 
lions of  miles,  without  ever  arriving  at  the  end  of  the 
progression.  It  is  not  difficult,  indeed,  to  carry  our 
conceptions  to  the  utmost  bounds  of  the  universe ;  at 
least  so  far  as  it  falls  within  our  notice.  But  then  the 
imagination  rests  not  here  ;  it  sees  immeasurable  spaces 
beyond,  capable  of  receiving  new  worlds,  which  it  can 
pursue,  as  rising  one  above  another  in  an  endless  suc- 
cession. This  consideration  of  space  ever  growing  on 
all  sides  of  us,  and  yet  never  to  be  exhausted,  is  that 
which  gives  us  the  idea  of  immensity  ;  which  is  in  fact 
nothing  else  but  the  infinity  of  number,  applied  to  cer- 
tain portions  of  extension,  as  miles,  or  leagues,  &c. 
and  these  conceived  as  extended  every  way  around  us, 
in  infinite  and  innumerable  right  lines. 

Sec.   XIV.   Compound  Ideas  resulting  from  the  Union 
of  Perceptions  of  different  Kinds. 

Hitherto  we  have  considered  the  mind  as  employed 
rrbout  one  and  the  same  idea,  enlarging  and  diversify- 
ing it  in  various  forms.  We  have  seen  it  rising  from 
the  most  simple  and  obvious  notices  to  the  conception 
of  infinity  itself  ;  and  taken  a  view  of  it  in  all  the  dif- 
ferent stages  of  its  improvement.  Let  us  now  proceed 
to  the  more  complicated  act  of  composition,  when  the 
mind  br'mgs  several  ideas  of  different  kinds  together, 
and  voluntarily  combines  them  into  one  complex  con- 
ception. Such  for  instance,  is  our  idea  of  a  tune,  as 
comprehending  a  variety  of  notes,  with  many  differ- 
ent modulations  of  sound.  And  here  it  is  to  be  observ- 
ed, that  though  the  complex  idea  may  be  excited  in  us, 
by  hearing  the  air  itself  struck  off  upon  a  proper  in- 
strument ;  yet,  considered  originally,  it  still  belongs 
to  this  class  of  perceptions,  which  are  distinguished  as 
the  arbitrary  collections  of  the  mind.  It  was  the  mu- 
sician, 01*  composer,  that  combined  the  several  notes, 
and  determined  the  order  in  which  they  were  to  follow 
one  another  ;  nor  had  that  peculiar  composition  of 
sounds  any  real  union  in  nature,  before  they  were  thus 


OF  LOGIC.  43 

brought  together  in  his  mind.  Of  the  same  nature  are 
most  of  our  ideas  of  human  actions  ;  for  though  many 
of  them  come  to  our  notice  by  seeing  the  actions  them- 
selves, or  hearing  them  described  by  others,  as  distil- 
ling, carvings  treason,  8cc.  yet  it  is  plain  that  they 
must  have  been  projected  and  contrived  in  the  mind  of 
man  before  they  had  a  real  existence. 
Sec.  XV..../fi?w  the  Mind  is  determined  in  making 
these  Combinations. 
It  is  here  that  the  understanding  has  the  greatest 
ficope,  and  finds  most  employment  for  its  active  powers : 
nor  indeed  i^  it  possible  to  set  any  bounds  to  the  ideas 
of  this  class  ;  the  combinations  already  made  being  al- 
most innumerable,  and  those  yet  in  the  power  of  the 
mind  affording  an  endless  diversity.  It  may  not,  how- 
ever, be  amiss  to  consider  how  we  conduct  ourselveg 
amidst  so  great  a  variety,  and  by  what  rules  we  pro- 
ceed in  making  those  combinations  to  which  we  have 
affixed  particular  names,  while  others,  perhaps,  no  less 
obvious,  are  neglected.  The  idea  of  killing,  for  in- 
stance, joined  to  that  of  a  father,  makes  a  distinct  spe- 
cies of  action,  known  by  the  name  of  parricide.  It  was 
doubtless  as  obvious  to  distinguish  between  the  killing 
of  an  old  man  and  a  child,  which  yet  we  find  is  not  done  ; 
both  these  actions  being  comprehended  under  the  ge- 
neral naro^flf  murder.  By  what  views  therefore  does  the 
mind  re^pfte  its  combinations?  Why  is  it  determined 
to  one  collection  of  ideas  rather  than  another?  This 
cannot  be  well  understood,  without  observing,  that  it 
is  the  end  of  language  to  communicate  our  thoughts 
one  to  another.  Words  are  the  signs  of  our  ideas,  and 
serve  to  express  the  conceptions  of  the  mind.  Now  it  is 
apparent,  that  such  conceptions  as  are  most  apt  to  occur 
in  the  commerce  of  life,  would  be  first  distinguished  by 
particular  names  ;  the  frequent  occasion  men  have,  of 
mentioning  these  among  themselves,  rendering  this  ab- 
solutely necessary.  But  as  many  of  these  conceptions 
are  collections  of  different  simple  ideas,  hence  we  are 
insensibly  led  to  sucli  peculiar  combinations,  as  are 
most  serviceable  to  purposes  of  mutual  intercourse  and 
communication. 


44  DUNCAN'S  ELEMENTS 

Sec   XV I... 'Ideas  of  Human  Actions  often  formed,  £<*- 
fore  the  Actions  themselves  exist* 

Let  us  suppose,  in  the  first  beginnings  of  society, 
a  company  of  legislators  met  together,  in  order  to  con- 
sult on  proper  regulations  for  the  government  of  the 
community.  If  they  are  men  of  prudence  and  foresight, 
they  will  naturally  observe  many  new  occurrences, 
likely  to  arise  from  this  coalition  of  mankind,  and 
their  living  together  in  crowds.  Perhaps  the  age  in 
which  they  live,  has  not  produced  an  instance  of  one 
man's  killing  ^another ;  yet  from  the  knowledge  of 
their  own  frame,  and  their  power  of  doing  hurt,  they 
conceive  this  as  a  possible  case,  and  are  wiliing  to  pro- 
vide against  it.  Thus  all  the  ideas  that  enter  into  the 
complex  one  of  murder,  are  brought  together,  and 
united  into  one  conception,  before  the  action  itself 
really  exists.  It  is  not,  however,  thought  necessary  to 
take  into  consideration  the  age  of  the  person  ;  the 
chief  thing  in  view  being  to  prevent  the  putting  an 
end  to  another's  life  unjustly,  whether  old  or  young  ; 
and  therefore  the  penalty  equally  effects  both  cases. 
But  when  they  come  to  consider  the  relation  in  which 
the  person  killed  may  stand  to  the  murderer,  here 
there  appears  a  manifest  difference  ;  as  it  adds  to  the 
crime,  when  committed  upon  a  benefactofl^  and  ren- 
ders it  particularly  heinous  in  the  case  ofa  father. 
This  last,  therefore,  is  made  to  constitute  a  distinct  spe- 
cies of  action,  and  lias  a  peculiar  punishment  allotted 
to  it.  Thus  we  see  how  men,  according  to  their  dif- 
ferent manner  of  life,  and  the  relations  they  stand  in 
to  one  another,  are  naturally  led  to  form  several  col- 
lections of  simple  ideas,  preferably  to  others,  as  fore- 
seeing they  may  have  frequent  occasion  to  take  notice 
of  such  precise  combinations.  And  because  it  would 
be  tedious  in  conversation,  every  time  these  complex 
notions  occur,  to  enumerate  all  the  ideas  of  which 
they  consist  ;  therefore,  for  the  sake  of  ease  and  dis- 
patch, they  give  them  particular  names,  and  thereby 
render  the  compositions  fixed  and  permanent. 


OF  LOGIC.  4$ 

Sec.  XVII....  Tta  necessity  of  Mutual  Intercourse^ 
and  Men's  particular  Aims  in  Life,  a  great  Source 
of  Complex  Ideas. 

That  it  is  in  this  manner  we  come  by  our  complex 
ideas,  which  multiply  upon  us  according  as  the  exi- 
gencies of  society  require,  or  our  pursuits,  method  of 
life,  and  different  aimsx  throw  occasions  in  our  way, 
of  combining  such  and  such  perceptions  together, 
might  be  easily  made  appear,  by  a  short  view  of  the 
combinations  themselves.  Human,  actions,  as  occur- 
ring most  frequently,  and  affording  large  matter  of 
conversation,  debate,  and  enquiry  among  men,  have 
been  very  nicely  modified,  and  distinguished  into 
classes,  according  to  the  several  circumstances  most 
likely  to  attend  them.  In  like  manner,  the  arts  and 
sciences,  in  proportion  as  they  are  cultivated,  leading 
us  into  many  compound  views  of  things,  which  other- 
wise  would  never  offer  themselves  to  the  considera- 
tion of  the  mind  ;  the  complex  ideas  of  this  sort, 
with  the  names  by  which  they  are  expressed,  are,  we 
find,  the  work  of  such  particular  nations,  where  these 
arts  and  sciences  have  chiefly  flourished.  The  Greeks, 
for  instance,  excelled  in  learning  and  polite  know- 
ledge ;  hence  many  of  the  terms  belonging  to  rhetoric, 
poetry,  philosophy,  physic,  See.  come  originally  from 
their  language.  Modern  fortification  has  received  its 
greatest  improvements  among  the  French;  and  ac- 
cordingly the  ideas  and  terms  of  the  art  are  mostly  der:-. 
ved  from  writers  of  that  nation.  In  Italy,  architec- 
ture, music,  and  painting,  have  been  the  great  exer- 
cise of  the  men  of  genius  ;  it  is  therefore  .among  them 
that  we  find  the  several  complex  notions  belonging  te 
these  parts  of  study,  as  well  as  the  names  by  which 
they  are  expressed  ;  nor  can  we  discourse  accurately 
and  minutely  of  the  above-mentioned  arts,  without 
having  recourse  to  the  language  of  that  climate.  And 
if  we  descend  into  the^particular  callings  and  profes- 
sions of  men,  they  have  all  their  peculiar  collections  of 
ideas,  distinguished  by  their  several  names,  and  hardly 
known  but  to  such  as  are  conversant  in  that  manner  of 


46  DUNCAN'S  ELEMENTS 

life.  Thus  calcination,  coliobation,  filtration,  £cc.-?.re 
■Words  standing  for  complex  ideas  frequently  framed  in 
the  minds  of  chymists,  and  therefore  familiar  to  men  of 
that  employment.  Yet  as  these,  and  such  like  com- 
binations, seldom  occur  in  common  life,  the  generality 
of  mankind,  we  see,  are  in  a  great  measure  unacquaint- 
ed with  them. 

Sec.  XVIII. ...Hence  different  Sets  of  theni  prevail  in 
different  Countries  :  and  Words  in  one  Language  have 
none  to  ansxver  them  in  another. 

I  might  pursue  these  speculations  farther,  and  shew 
how  the  several  fashions,  customs,  and  manners  of  one 
nation,  leading  them  to  form  many  complex  notions 
"which  come  not  so  naturally  in  the  way  of  another  ; 
different  sets  of  ideas  prevail  in  different  countries, 
and  of  course  have  names  appropriated  to  them  in 
the  language,  to  which  there  are  no  words  that  an- 
swer in  another.  The  procedure  and  forms  cf  our 
courts  of  justice  have  introduced  many  terms  into  the 
English  law,  which  stand  for  collections  of  ideas  framed 
among  no  other  people.  Nor  would  it  be  possible  to  ren- 
der these  terms  by  any  single  words  of  another  lan- 
guage;  because,  where  ideas  themselves  prevail  not, 
there  are  no  names  provided  to  express  them.  In  this 
case,  therefore,  it  becomes  necessary  to  use  circumlo- 
cutions, and  enumeraie  the  several  ideas  comprehended 
in  the  collection,  if  we  would  so  express  ourselves,  as 
to  be  understood  in  the  language  of  other  nations. 
Kay,  even  among  the  same  people,  the  change  of  cus- 
toms and  opinions  frequently  brings  new  sets  of  ideas, 
"which,  of  course,  must  be  distinguished  by  particular 
names  ;  while,  at  the  same  time,  the  notions  of  former 
ages  grow  into  disuse,  and  the  words  answering  them 
are  wholly  laid  aside,  or  employed  in  a  signification  dif- 
ferent from  what  they  had  before. 

See.     XIX....77i/.r,    too,   the  cause   that  Languages 
are  in  a  perpetual  Jlux. 
Thus  languages  are  in  a  perpetual  flux,  and  by  de- 
grees vary  so  much  from  their  original  frame,  as  to  be- 
come unintelligible  even  to  the  descendants  of  those 


OF  LOGIC.  47 

who  speak  them.  If  we  run  back  into  the  ages  of  chi* 
valry  in  England,  when  tilts  and  tournaments  were  in 
fashion,  how  many  complex  ideas,  peculiar  to  that  mode 
of  life,  shall  we  find  familiar  among  the  men  of  those 
times,  which  are  now  little  known  or  attended  to?  On 
the  contrary,  the  improvements  in  arts  and  sciences 
that  have  since  taken  place,  have  hd  us  into  innumerab- 
le views  of  things,  to  which  our  fore-fathers  were  per- 
fect strangers.  But  I  shall  not  push  these  reflections  any 
farther,  believing  that  what  has  been  said  will  be  suffi- 
cient to  show  the  origin  and  progress  of  our  compound 
ideas,  and  how  the  mind  is  directed  in  the  choice  of  the 
combinations  it  makes.  We  therefore  proceed  to  the 
consideration  of  abstract  ideas,  which  make  the  sub- 
ject of  the  following  article. 


ART.  II. 


OF  ABSTRACT  OR  UNIVERSAL  IDEAS. 

Sec.  L.^Gencral  Ideas  formed  by  the  Abstraction  of 
the  Mind. 

HAVING  dispatched  what  was  necessary  to  be  said 
concerning  our  compound  ideas,  considered  mere- 
ly as  they  are  combinations  of  the  understanding,  it  is 
now  time  to  explain  how  we  come  by  our  general  no- 
tions which  serve  to  represent  to  us  a  multitude  of  in- 
dividuals and  are  the  standards  by  which  we  rank  things 
into  sorts.  And  this,  as  we  have  before  intimated,  is 
done  by  the  abstraction  of  the  mind;  which  act  may- 
be extended  to  all  our  ideas,  whether  simple,  compound, 
or  of  substances.  Ifj  for  instance,  we  fix  our  attention 
on  any  particular  colour,  as  scarlet,  we  can  leave  out 
the  consideration  of  all  present  circumstances,  as  the 
subject  in  which  it  inheres,  the  time  and  place  of  seeing 
it,  Sec.  and  retaining  only  the  impression  itself,  make^ 
it  a  representative  cf  that  quality  or  appearance,  where  - 
ever  we  chance  to  meet  with  it.  It  is  thus  that  abstract 
and  universal  ideas  are  framed ;  for  the  mind  regarding 
fciiiy  the  scarlet  colour,  which  one  day  it  observes  per- 


48  DUNCAN'S  ELEMENTS 

haps  in  a  piece  of  cloth,  another  in  a  picture,  and  a 
third  in  the  rainbow;  the  appearance  is  conceived  to 
be  the  same  in  all  these  objects,  and  therefore  is  called 
by  the  same  name. 

Sec,  II.... A 11  the  Perceptions  of  the  Understanding 
particular* 
But  to  enter  a  little  more  closely  into  this  matter,  and 
show  that  these  our  general  conceptions  are  the  mere 
creatures  of  the  understanding,  it  may  not  be  amiss  to 
take  notice,  that  all  our  perceptions  of  things,  whether 
we  derive  them  from  sensation  or  reflexion,  are  of  their 
own  nature  particular^  and  represent  to  us  single,  de- 
terminate objects.  When  we  see  a  horse,  for  instance, 
in  the  fields,  our  idea  is  that  of  an  individual.  If  we 
hear  a  sound,  it  is  something  particular,  and  different 
from  what  we  hear  at  any  other  time.  Every  percep- 
tion of  the  mind  is  distinct  from  every  other  perception; 
nay,  and  every  idea  brought  into  view  by  the  imagina- 
tion, as  when  we  frame  the  image  of  a  lion  standing 
before  us,  is  still  singular,  and  represents  a  single  object. 

Sec.  IIL«««77t?  Idea  of  the  Species  represents  what  is 
common  to  different  individuals* 
But  when  we  come  to  take  a  view  of  these  several 
particulars,  we  readily  observe  among  some  of  them 
a  resemblance  ;  and  framing  to  ourselves  an  idea  of 
those  things  in  Which  any  of  them  are  found  to  agree, 
we  thereby  get  a  general  notion,  applicable  to  many 
individuals.  Thus  horses  are  found  to  resemble  one 
another  in  shape,  voice,  and  structure  of  parts.  The 
idea,  which  takes  in  only  the  particulars  of  this  resem- 
blance, excluding  what  is  peculiar  to  each  single  ani- 
mal, becomes  of  course  common  to  all  creatures  of 
that  kind,  and  is  therefore  the  representative  of  a 
whole  class  of  beings.  Accordingly  the  name  of  that 
general  idea  is  given  to  every  animal  in  which  that 
shape,  voice,  and  structure  is  found;  for  the  word 
horse,  implying  only  these  particulars,  must  belong  to 
all  creatures  wherein  they  exist.  This  is  the  first  step 
or  gradation  in  the  forming  of  abstract  notions,  when 
tfee  mind  confines  itself  textile  consideration  of  indiyi* 


OF  LOGIC.  49 

duals,  and  frames  an  idea  that  comprehends  such  only 
under  it.  The  rank  or  class  of  things  answering  to 
this  idea,  is  called  species  in  the  language  of  the 
schools.  So  a  horse  is  a  certain  species  of  animals,  an 
oak  is  a  species  of  trees,  and  a  square  is  a  species  of 
four-sided  figures. 

Sec.  IV....  The  Idea  of  the  Genus  represents  what  us 
common  to  several  Species. 
When  we  have  thu3  learned  to  rank  individuals  into 
sorts  and  classes,  according  to  the  resemblance  found 
among  them,  the  mind  proceeds  next  to  consider  the 
species  themselves,  and  often  in  these  too  observes  a 
certain  likeness.  Whereupon,  throwing  out  all  those 
particulars  wherein  the  several  species  are  found  to 
disagree,  and  retaining  only  such  as  are  common  to 
them  all,  we  thereby  frame  a  still  more  general  idea, 
comprehending  under  it  a  variety  of  different  species. 
Thus  a  sparrow,  a  hawk,  and  eagle,  &c.  are  distinct 
species  of  birds,  which  have  each  their  peculiar  shape 
and  make.  They  nevertheless  resemble  one  another, 
in  being  covered  with  feathers, and  provided  with  wings 
that  bear  them  through  the  air.  Out  of  these  parti- 
culars we  form  a  new  idea,  including  all  the  common 
properties  of  the  feathered  kind  ;  and  appropriating  to 
it  the  name  of  bird,  mark  by  that  word  another  class  of 
things,  of  a  higher  order  than  any  of  the  former.  This 
superior  division,  which  extends  to  several  species  at 
once,  is  called  in  the  schools  the  genus,  and  is  the  second 
step  the  mind  takes  in  advancing  to  universal  notions. 

Sec.  V.. ..The  Mind  may  advance  by  manifold  Grada- 
tions, in  rising  from  Particulars'  to  Generals. 
And  thus  have  I  given  a  short,  but  I  hope  intelligi- 
ble account,  of  the  business  of  genera  and  species,  about 
which  so  much  has  bee»  said  in  the  writings  of  logici- 
ans. Species,  \n  strictness  and  propriety  of  speech,  is 
such  a  rank  or  class  of  things,  as  comprehends  under 
it  only  individuals  :  genus  advances  still  higher,  and 
takes  in  a  variety  of  distinct  species.  It  is,  however,  to 
be  observed,  that  the  mind  in  rising  from  particulars 
.to  generals,  dees  not  confine  itself  to  cue  or  two  gra- 

E 


30  DUNCAN'S  ELEMENTS 

dations,  but  may  carry  its  views  through  the  whole 
extent  ©f  things,  until  at  length  it  arrive  at  an  idea 
embracing  the  universal  compass  of  nature.  For  when 
■we  have  ranked  things  into  sorts,  and  reduced  these 
again  to  the  higher  order  or  ge?ius,  these  genera  are 
still  found  to  resemble  one  another  in  some  particu- 
lars, which  being  collected  into  one  idea,  form  a  new 
and  more  comprehensive  division  of  things.  Thus 
Urd  is  a  genus,  embracing  all  the  varieties  of  the  fea- 
thered kind.  Fish  implies  the  several  species  of  living 
creatures  which  inhabit  the  waters.  Quadruped  and 
insect  are  also  universal  ideas,  that  take  in  many  infe- 
rior distributions  and  classes.  Yet  all  these  different 
orders  of  being,  have  this  in  common,  that  they  are 
provided  with  organical  bodies,  fitted  for  the  purposes 
of  life  and  spontaneous  motion.  An  idea,  therefore, 
comprehending  only  these  last  particulars,  will  equally 
belong  to  all  the  divisions  before  enumerated  ;  and  the 
■word  animal^  by  which  it  is  expressed,  becomes  a  gene- 
ral name  for  the  several  creatures  endued  with  life, 
sense,  and  spontaneous  motion.  If  we  are  for  carry- 
ing our  views  still  farther,  and  framing  a  yet  more  uni- 
versal notion,  we  can  cast  our  eyes  upon  both  the  ani- 
mate and  inanimate  parts  of  nature  ;  wherein  we  find 
this  mutual  correspondence,  that  they  exist,  and  con- 
tinue in  being.  This  last  idea,  therefore,  of  being  in 
general,  comprehends  under  it  all  the  varieties  of 
things,  and  may  be  universally  applied  to  whatever 
has  either  life  or  existence  ;  so  that  in  respect  of  the 
present  frame  of  nature,  it  is  tjie  highest  and  most  uni- 
versal idea  we  have. 

Sec*  VI... .Whence  many  intermediate  Steps  betnveenthc 
highest  Genus  and  lowest  Species. 

In  this  series  of  notions,  rising  one  above  another, 
in  the  degree  of  universality  ;  that  division,  which 
comprehends  under  its  several  genera,  is  called  in  the 
schools  the  higher  genus  ;  which  denomination  conti- 
nues, until  wc  arrive  at  the  last  advance  of  the  under- 
standing, when,  being  come  to  the  most  general  of  all 
ideas,  that  admits  not  of  a  superior,  it  is  distinguished 


OF  LOGIC,  51 

fey  the  name  of  the  genus  generalissimum*  In  like  man- 
ner the  several  genera,  comprehended  under  a  higher 
genus,  are,  in  respect  of  it,  considered  as  species  ;  and 
as  these  two  last  have  species  under  them,  the  inferior 
divisions  are,  for  distinction's  sake,  termed  lower  spe- 
ties.  Thus  the  progression  continues,  and  when  we 
come  to  the  lowest  subdivision  of  all,  comprehending 
only  individuals,  which,  as  I  have  before  intimated, 
constitutes  the  proper  species,  this  the  schools  denomi- 
nate the  species  specialissima.  All  that  lie  between 
it  and  the  highest  distribution  of  things,  are  the  inter- 
mediate genera  and  species,  which  are  termed,  each  in 
their  turn,  genus  gener alius,  or  species  specialior,  ac- 
cording as  we  consider  them  in  the  ascending  or  de- 
scending scale  of  our  ideas  ;  or,  to  speak  in  the  lan- 
guage of  logicians,  according  to  their  ascent  or  descent 
in  linea  prtdicamentali.  1  should  net  have  entered  so 
far  into  these  verbal  disquisitions,  had  not  the  terms 
here  explained,  been  such  as  frequently  occur  in  the 
writings  of  philosophers  ;  insomuch  that  without  some 
knowledge  of  them  we  must  often  be  at  a  loss,  in  the 
prosecution  of  these  studies.  Besides,  it  is  both  curious 
and  useful,  to  see  the  gradual  progress  of  the  mind,  in 
its  advances  from  particular  to  general  conceptions— 
to  observe  it  ranging  its  ideas  into  classes,  and  esta- 
blishing a  just  and  regular  subordination  in  its  views 
and  notices  of  things.  This  is  the  shortest  way  to 
knowledge,  and  affords  the  best  means  of  preserving  the 
order  and  due  connexion  of  our  thoughts,  so  as  to 
make  them  subservient  to  the  increase  of  science.  For 
when  we  see  how  things  comprehend, '  or  are  compre- 
hended in,  one  another,  we  are  able  to  discover  the  mu- 
tual dependence  of  all  the  several  branches  of  know- 
ledge which  leads  us  into  the  true  and  natural  method  of 
conducting  our  understandings  in  the  search  of  truth. 
Sec.  VU....G<7i<?ra/  Ideas  the  Creatures  of  the  Under* 
standing. 
From  what  has  been  said,  it  is  evident,  that  gene- 
ral ideas'  are  the  creatures  and  inventions  oi  the  under- 
standing. Nature,  it  is  true,  in  the  production  of 
things,  makes  many  of  them  alike  ;  but  it  is  the  mind 


52  DUNCAN'S  ELEMENTS 

alone,  that  collects  the  particulars  in  which  they  agree? 
into  one  idea,  and  sets  it  up  as  a  representative  of  ma- 
ny individuals.  And  now  1  think  we  may  venture  upon 
that  much-agitated  question,  where  do  the  genera  and 
species  of  things  exist  ?  To  which  I  answer,  in  the 
mind.  Universality  belongs  not  to  things  themselves,  it 
being  apparent,  that  they  are  all  particular  in  their  ex- 
istence. However,  as  they  often  have  many  properties 
in  common,  the  understanding,  by  uniting  these  into 
one  conception,  obtains  a  general  idea,  under  which  it 
Tanks  all  the  several  objects  wherein  these  properties 
are  found.  So  far  indeed  we  must  allow,  that  the  par- 
ticular combination  of  properties,  which  constitutes  the 
genus  or  species,  exists  in  all  the  individuals  referred  to 
that  genus  or  species  ;  but  then  it  is  in  conjunction  with 
other  properties,  by  which  these  individuals  are  distin- 
guished from  one  other.  Thus  the  collection  of  simple 
ideas,  signified  by  the  word  bird,  is  to  be  found,  for  in- 
stance, in  a  hawk,  or  any  other  single  animal,  to  which 
we  apply  that  general  name:  but  the  notion  itself,  ab- 
stracted from  all  the  particulars  to  which  it  belongs, 
has  evidently  no  existence  out  of  the  understanding. 
There  is  not  a  being  in  nature  that  can  be  called  a  bird 
in  general,  or  that  does  not  necessarily  imply,  in  the 
very  conception  of  it,  several  simple  ideas,  besides  those 
marked  by  that  word.  For  the  name,  in  this  case,  sig- 
nifies no  more  than  an  animal  covered  with  feathers,  and 
provided  with  wings,  without  regard  either  to  shape, 
bulk,  or  the  particular  time  and  place  of  its"existence. 
These  last  considerations,  however,  are  inseparable 
from  the  reality  of  things,  and  therefore  must  be  added 
to  the  general  idea,  before  we  can  conceive  any  thing 
conformable  to  it  actually  brought  into  being. 
Sec.  VIII... .Considered  apart,  they  exist  only  in  the 
Mind,  but  in  conjunction  with  other  Ideas  in  the  in- 
dividuals comprehended  under  them. 
Hence  we  see  at  once,  what  sort  of  an  existence  ge- 
neral natures  have.  Considered  apart,  and  by  them- 
selves, they  are  wholly  the  workmanship  of  the  under- 
standing, and  derive  their  being  and  reality  from  it  ; 
but  viewed  in  conjunction  with  other  ideas  that  co-exist 


OF  LOGIC.  53 

with  them  in  the  several  objects  of  nature,  they  are  to 
be  found  in  the  individuals  to  which  they  refer ;  and 
therefore,  according  to  this  way  of  conception,  may  be 
said  to  have  an  existence  in  them.  Thus,  so  long  as 
the  ideas  answering  to  the  words  man  or  tree,  continue 
general  and  undetermined,  they  have  no  real  objects' 
answering  them  in  nature  ;  nor  can  the  collections  o£ 
simple  ideas,  marked  by  these  names,  while  all  others 
are  supposed  excluded,  exist  any  where  out  of  the  un- 
derstanding. Nevertheless,  as  all  the  simple  ideas,  in- 
cluded in  the  general  notion  of  man,  are  to  be  found  in 
every  particular  man — and  all  those  implied  in  the  no- 
tion of  a  t recy  in  every  particular  tree — hence  the  general 
nature  of  man,  exists  in  every  individual  man,  as  does 
the  general  nature  of  a  tree,  in  every  individual  tree. 
Sec.  IX. ...  Difference  of  Ideas  considered  as  compound 
and  as  universal. 
One  thing  still  remains  to  be  observed,  with  regard 
to  these  our  general  ideas ;  that,  though  many  of  therm 
are  evidently  combinations  of  different  simple  ideas,  and 
according  to  that  way  of  considering  them,  are  includ- 
ed in  the  first  division  of  our  complex  conceptions,  those, 
namely,  framed  by  the  composition  of  the  mind  ;  yet 
we  are  carefully  to  distinguish  between  an  idea,  as  it  is 
compound,  and  as  it  is  universal.  In  the  first  case,  the 
mind  chiefly  considers  the  several  ideas  that  are  com- 
bined together;  or,  in  other  words,  all  the  attributes, 
qualities,  or  parts,  that  are  contained  in  any  idea.  Thus 
the  idea  of  a  bird,  includes  life,  sense,  spontaneous  mo- 
tion, a  covering  of  feathers,  wings.  &x.  none  of  which 
can  be  left  out  without  destroying  the  very  nature  o£ 
the  idea,  and  making  it  something  quite  different  from 
what  it  was  before.  This  way  of  considering  things 
according  to  the  number  of  their  parts  and  properties, 
is  called  by  logicians  the  comprehension  of  an  idea.  But 
the  universality  of  our  notions  implies  quite  another 
turn  of  thinking,  in  as  much  as  it  fixes  the  regard  of 
the  mind,  upon  the  subject  to  which  our  ideas  extend, 
or  the  individuals  and  species  comprehended  under  them. 
In  this  sense,  the  idea  answering  to  the  word  bird,  takes 
in  the  several  species  of  the  feathered  creation,  the/raw^ 
K    9 


54  DUNCAN'S  ELEMENTS 

the  eagle,  sparrow,  lark,  and  innumerable  others,  to  all 
which  it  may  with  equal  propriety  be  applied.  And 
here  it  is  remarkable,  that  the  idea  loses  nothing  of  its 
force  or  comprehension,  by  being  restricted  to  a  parti- 
cular kind.  When  I  say  the  bird  of  Jove,  though  in 
this  case  the  idea  is  restrained  to  the  eagle  alone,  it  still 
remains  as  distinct,  and  includes  as  many  simple  ideas 
in  its  composition,  as  when,  before,  it  was  extended  to 
all  the  different  tribes  of  feathered  animals. 
Sec.  X...  The  comprehension  and  extension  of  our  Ideas* 
We  see,  therefore,  that  our  compound  ideas  may 
continue  t»he  same  in  respect  of  their  attributes,  or  the 
number  of  parts,  and  yet  vary  considerably  in  the  degree 
of  universality.  The  general  idea  of  man  is  the  same, 
whether  applied  to  the  whole  human  race,  or  those  of 
any  particular  nation.  When  I  affirm,  for  instance,  of 
mankind  in  general,  that  their  knowledge  falls  short  of 
perfection,  and  afterwards  make  the  like  observation  of 
the  men  of  the  present  age ;  in  both  cases,  the  word 
fnan  stands  for  one  and  the  same  collection  of  simple 
ideas;  but  in  respect  of  the  individuals  to  which  it  is 
applied,  there  is  a  great  and  manifest  difference.  That 
is,  the  term,  man,  denotes  one  invariable  compound 
idea;  which,  notwithstanding,  considered  as  a  general 
notion,  may  be  contracted  or  enlarged  at  pleasure. 
And  as  in  the  former  case,  the  several  parts  of  the'  com- 
pound idea  are  called  its  comprehension ;  so  in  the  lat- 
ter, the  individuals,  to  which  the  universal  idea  is  ap- 
plied, are  called  its  extension.  I  might  add  many  more 
observations  on  this  subject,  but  choose  rather  to  stop 
here,  having  said  enough  to  explain  the  difference  be- 
tween compound  and  abstract  ideas,  and  show  the  rea- 
son of  my  ranging  them  under  distinct  heads. 


ART.   III. 


OF  OUR  IDEAS  OF  RELATIONS. 

Sec.   I.,., Ideas  of  Relations  exceeding  numerous, 
[  GOME  now  to  the  third  and  last  division  of  those 
L  ideas,  which  I  consider  as  the  creatures  and  work- 


OF  LOGIC.  55 

manship  of  the  understanding  ;  such,  namely,  as  arise 
from  the  comparing  of  things  one  with  another.  For 
the  mind,  in  its  views,  is  not  tied  to  single  objects  ;  but 
can  examine  their  references  and  respects,  in  regard  to 
others,  brought  under  consideration  at  the  same  time. 
And  when  it  docs  so,  and  thence  derives  new  notices  of 
things,  the  ideas  thus  got  are  called  relations,  and  make, 
I  am  apt  to  think,  the  largest  class  of  all  our  percep- 
tions. For  every  single  object  will  admit  of  almost  in- 
numerable comparisons  with  others,  and  in  this  sense 
may  become  a  very  plentiful  source  of  ideas  to  the  un- 
derstanding. Thus,  if  we  compare  one  thing  with  ano- 
ther, in  respect  of  bulk,  we  get  the  ideas  of  greater,  less, 
or  equality  ;  if  in  respect  of  time,  of  older  and  younger  $ 
and  so  for  other  relations,  which  we  can  pursue  at  plea- 
sure, almost  without  end  ;  whence  it  is  easy  to  conceive, 
how  very  extensive  this  tribe  of  our  perceptions  must  be. 
Sec.  II. ...Men  chiefly  determined  to  particular  Com" 
parisons  by  4 he  Wants  and  Exigencies  of  Life. 
I  shall  not  pretend  to  trace  out  these  ideas  particu- 
larly, nor  indeed  so  much  as  to  enumerate  their  several 
divisions ;  it  being  enough  to  observe,  that  here,  as 
well  as  in  the  other  kinds  of  our  complex  ideas,  we 
bound  ourselves,  for  the  most  part,  to  such  comparisons, 
as  the  exigencies  of  society,  the  wants  of  life,  and  the 
different  professions  of  men,  render  necessary  ;  and  are 
more  or  less  accurate  in  tracing  out  the  relations  of 
things,  according  to  the  degree  of  importance  they 
appear  to  have  in  these  respects.  The  relations  of 
men  one  to  another,  arising  either  from  the  ties  of  blood, 
their  several  ranks  and  places  in  the  community,  or  a 
mutual  intercouse  of  good  offices,  being  of  great  weight 
and  concern  in  the  commerce  of  life,  have  in  a  particu- 
lar manner  engaged  our  attention,  and  are  therefore 
very  minutely  described.  For  the  same  reason,  men 
have  found  it  necessary,  to  determine,  as  exactly  as 
possible,  the  various  dependence  of  things,  as  their 
happiness  is  nearly  connected  with  this  knowledge. 
When  we  consider  objects  merely  in  respect  cf  exist- 
ence, as  either  giving  or  receiving  it,  we  come  by  the 
ideas  of  cause  and  effect ;  nor  need  1  mention  how  muck 


56  DUNCAN'S  ELEMENTS 

the  welfare  of  mankind  depends  on  an  extensive  view 
of  things,  as  they  stand  connected  in  this  relation  ;  it 
being  evident,  that  the  several  schemes  and  purposes  of 
life,  are  all  conducted  upon  a  previous  supposition,  that 
certain  known  causes  will  have  their  usual  regular  ef- 
fects, and  such  and  such  actions  be  attended  with  such 
and  such  consequences. 
Sec.  Ill,*; Relations  of  Creator  and  Creature^  Istcm 
But  there  are  other  relations  of  this  kind,  besides 
those  that  regard  merely  existence  ;  as  when  we  also 
take  into  the  account  the  additional  gifts  of  a  capa- 
city for  happiness,  and  the  means  of  attaining  it  ; 
which  constitutes  the  relation  of  Creator  and  creature*) 
in  the  more  solemn  acceptation  of  these  words.  Again, 
when  we  consider  the  great  Author  of  our  being,  not 
only  as  the  Creator  of  the  universe,  but  also  as  pre- 
serving and  holding  it  together,  and  presiding  over  the 
present  frame  of  things  with  uncontrouled  dominion  \ 
he  then  appears  under  the  notion  of  a  moral  G 'over -nor , 
to  whom  we  are  accountable  for  our  actions,  and  the 
use  we  make  of  those  powers  and  faculties  we  derive 
from  him.  Now  as  it  is  of  the  highest  consequence 
for  men,  not  to  be  unacquainted  with  these,  and  such 
like  relations  ;  hence  we  find,  that  the  wisest  nations, 
and  such  as  best  understood  the  true  application  of  the 
powers  of  the  mind,  have  always  made  it  their  chief 
study  to  regulate  and  ascertain  these  ideas,  and  trace 
them  in  all  their  consequences.  And  thus  we  may,  in 
some  measure,  perceive,  how  the  mind  proceeds  in 
comparing  its  ideas  together,  and  by  what  views  it  is 
chiefly  governed,  in  framing  the  complex  notions  of  this 
class,  by  which  it  represents  the  various  habitudes  of 
things,  I  shall  only  add  upon  this  subject,  these  two 
observations. 

Sec.  IV...0«r  Ideas  of  relations  very  clear  and  distinct* 
First,  that  our  ideas  of  relations,  are  for  the  most 
part  very  clear  and  distinct.  For  the  comparing  of 
things  together,  being  a  voluntary  act  of  the  mind, 
we  cannot  but  suppose  that  it  must  be  acquainted  with 
its  own  views  in  the  comparison ;  and  of  course  have 
a  clear  conception  of  the  foundation  of  that  relation, 


OF  LOGIC.  sr 

it  sets  itself  to  enquire  into.  Thus  the  relation  of 
cause  and  effect,  implying  only  that  one  thing  produ- 
ces, or  is  produced  by  another,  which  notions  are  al- 
ways distinctly  settled  in  the  understanding  before  it 
goes  about  to  make  the  comparison  ;  it  is  evident, 
that  the  idea  representing  this  mutual  respect  of  ob- 
jects, -will  be  no  less  clear,  than  are  the  notions  them- 
selves upon  which  the  relation  is  founded.  And  what 
is  still  more  remarkable  of  the  ideas  of  this  class  ; 
they  cease  not  to  be  distinct,  even  where  the  subjects 
compared  are  but  very  imperfectly  known.  For  1  can 
well  enough  conceive,  that  one  thing  has  produced 
another,  and  that  therefore  they  stand  related  as  cause 
and  effect,  though  my  ideas  of  the  things  themselves 
may  perhaps  be  very  obscure,  and  come  far  short  of 
representing  their  real  nature  and  properties.  I  doubt 
not  but  it  will  be  readily  owned,  that  our  idea  of  the 
universe,  considered  as  comprehending  the  whole 
frame  of  created  things,  is  very  inadequate  ;  and  I 
think  it  is  still  more  apparent,  that  our  notion  of  the 
Supreme  Being  comes  not  up  to  the  excellence  and 
perfection  of  his  nature.  Yet  we  very  well  -understand 
what  is  meant  by  calling  God  the  Author  of  the 
world  ;  and  though  we  comprehend  not  the  manner 
of  his  producing  it,  find  no  difficulty  in  framing  the 
ideas,  the  relative  words  Creator  and  creature  stand  for. 

Sec.  V,. ..Ideas  of  Relations  among  the  most  important 
Conceptions  of  the  Mind* 

I  have  yet  another  observation  to  make  upon  this 
subject  ;  and  it  is,  that  our  ideas  of  relations  are  among 
the  most  important  conceptions  of  the  understanding, 
and  afford  the  largest  field  for  the  exercise  and  im- 
provement of  human  knowledge.  Moat  of  our  en- 
quiries regard  relative  ideas,  and  are  set  on  foot  with 
a  view  to  investigate  the  mutual  habitudes  of  things. 
The  mathematician  has  taken  quantity  for  his  province, 
and  teaches  us  how  to  compare  magnitudes  of  differ- 
ent figures  and  dimensions,  in  order  to  judge  with 
certainty  of  their  relative  properties.  The  philosopher 
attaches  himself  to  the  chain  of  causes  and  effects,  and 


58  DUNCAN'S  ELEMENTS 

endeavours  to  trace  out  the  various  dependence  of 
things  considered  in  this  li$$it.  In  fine,  whither  do 
all  our  researches  tend,  But  by  means  of  certain 
known  properties  and  relations,  to  find  out  others  that 
stand  some  how  connected  with  them  ?  As  for  the 
importance  of  these  conceptions,  no  one  can  call  that 
in  question,  who  reflects  ;  that  from  our  relations  to 
our  Creator  and  one  another,  arise  all  the  duties  of 
morality  and  religion,  and  that  the  correspondence  of 
the  several  objects  of  nature,  to  the  organs  of  the 
body,  and  faculties  of  the  mind,  is  that  by  which 
alone  we  can  judge  of  what  will  procure  us  happiness 
or  misery.  Whence  it  is  evident,  that  without  an 
exact  knowledge  of  these  relations,  we  must  wander 
on  in  life  with  great  uncertainty,  and  may  often  plunge 
into  calamities  and  misfortunes,  by  those  very  pur- 
suits from  which  we  expected  nothing  but  joy  and 
pleasure. 

Sec.  VI... •Recapitulation. 

Thus  have  I  gone  through  the  several  divisions  of 
our  iaeas,  which  I  have  endeavoured  to  represent  in 
such  a  manner  as  their  vast  extent  may  most  easily  ap- 
pear, and  the  conduct  of  the  mind  in  framing  them 
be  distinctly  apprehended.  I  might  easily  run  into 
other  distinctions,  by  considering  them  as  clear  or 
obscure,  adequate  or  inadequate,  true  or  false.  But 
the  limits  of  this  tract  will  not  allow  my  entering 
more  fully  into  the  subject,  and  I  think  it  the  less 
needful,  because  the  very  names  are  almost  sufricieat 
to  convey  a  noticn  of  these  several  kinds  of  ideas  into 
the  mind.  But  as  the  division  explained  above  seems 
to  be  of  great  importance,  towards  settling  in  the  un- 
derstanding a  just  view  of  the  progress  of  human  know- 
ledge, and  the  steps  by  which  it  advances  from  one 
degree  of  improvement  to  another,  I  shall  here  run 
over  it  again  in  as  few  words  as  possible,  that  the 
whole  process  may  be  seen  at  once.  Our  ideas  are  all 
derived  into  the  understanding,  either  by  sensation  or 
reflexion.  This,  however,  is  observable,  that  one  and 
the  same  object  often  excites  a  variety  of  perceptions 


OF  LOGIC,  3$ 

at  once,  which  are  nevertheless  readily  distinguish- 
ed by  the  mind,  and  appear  each  under  a  farm  pe« 
culiar  to  itself.  These  constitute  our  primary  and 
original  notices,  and  are  easily  known  from  all  others, 
in  as  much  as  they  are  entirely  void  of  plurality,  and 
cannot  be  divided  into  two  or  more  different  ideas. 
They  are  also  the  materials  out  of  which  the  others 
are  formed,  and  are  therefore,  by  way  of  distinction, 
called  simple  ideas.  But  the  mind,  though  it  has  no 
power  over  these,  either  to  fashion  or  destroy  them, 
can  yet  combine  them  in  an  infinite  number  of  ways  ; 
and  from  their  various  combinations  result  all  our 
complex  ideas,  which  are  of  two  principal  kinds.  First, 
such  as  are  derived  from  without,  and  represent  those 
combinations  of  simple  ideas,  that  have  a  real  existence 
in  nature.  Of  this  sort  are  all  our  ideas  of  substances. 
Secondly,  the  conceptions  formed  by  the  mind  itself, 
arbitrarily  uniting  and  putting  together  its  ideas.  And 
as  this  makes  by  far  the  largest  class,  and  comprehend* 
all  those  ideas  which  may  be  properly  termed  our  own, 
as  being  the  real  workmanship  of  the  understanding ;  so 
they  fall  very  naturally  under  three  distinct  heads.  For 
either  the  mind  combines  several  simple  ideas  together, 
in  order  to  form  them  into  one  conception,  in  which 
the  number  and  quality  cf  the  ideas  united,  are  prin- 
cipally considered  ;  and  thus  it  is  we  come  by  all  our 
compound  notions  :  or  it  fixes  upon  any  of  its  ideas, 
whether  simple,  compounder  of  substances  ;  and,  leav- 
ing out  the  circumstances  of  time,  place,  real  exist- 
ence, and  whatever  renders  it  particular,  considers  the 
appearance  alone,  and  makes  that  a  representative  of 
all  of  the  kind  ;  whence  our  abstract  and  universal 
ideas  are  derived  :  or  lastly,  it  compares  things  one 
with  another,  examines  their  mutual  connexions,  and 
thereby  furnishes  itself  with  a  new  set  of  notions, 
known  by  the  name  of  relations,  which,  as  has  been  al- 
ready remarked,  make  by  no  means  the  least  important 
class  of  our  perceptions.  This  division  of  our  ideas, 
as  it  seems  to  be  the  most  natural,  and  truly  to  repre- 
sent the  manner  in  which  they  are  introduced  into  the 
«iind;  so  1  believe  it  will  be  found  to  comprehend  them 


60  DUNCAN'S  ELEMENTS 

in  all  their  varieties.  I  shall  therefore  now  proceed  to 
offer  some  observations  upon  language,  as  being  the 
great  instrument,  by  which  we  are  enabled  to  make  our 
ideas  and  perceptions  known  to  others* 


Cfjap,  V. 

OF  WORDS,  CONSIDERED  AS  THE 
SIGNS  OF  OUR  IDEAS. 

Sec.  I Words  furnish  the  Means  of  recording  our 

own  'Thoughts* 

WE  have  seen  how  the  mind  comes  to  be  first 
furnished  with  ideas,  and  by  what  methods  it 
contrives  to  diversify  and  enlarge  its  stock  :  let  us  now 
consider  the  means  of  making  known  our  thoughts  to 
others,  that  we  may  not  only  understand  how  know- 
ledge is  acquired,  but  also  in  what  manner  it  may  be 
communicated  with  the  greatest  certainty  and  advan- 
tage. For  our  ideas,  though  manifold  and  various,  are 
nevertheless,  all  within  our  own  breasts,  invisible  to 
others,  nor  can  of  themselves  be  made  appear.  But 
God  designing  us  for  society,  and  to  have  a  fellowship 
with  those  of  our  kind,  has  provided  us  with  organs  fit- 
ted to  frame  articulate  sounds,  and  given  us  also  a  ca- 
pacity of  using  those  sounds  as  signs  of  internal  con- 
ceptions. Hence  ppring  words  and  languages  ;  for 
having  once  pitched  upon  any  sound,  to  stand  as  the 
mark  of  an  idea  in  the  mind,  custom^  by  degrees,  estab- 
lishes such  a  connexion  between  them,  that  the  appear- 
ance of  the  idea  in  the  understanding  always  brings 
to  our  remembrance  the  sound  or  name  by  which  it  is 
expressed  ;  as,  in  like  manner,  the  hearing  of  the  sound 
newer  fails  to  excite  the  idea  for  which  it  is  made  to 
stand.  And  thus  it  is  easy  to  conceive,  how  a  man 
may  record  his  own  thoughts,  and  bring  them  again 
into  view,  in  any  succeeding  period  of  life.  For  this 
connexion  being  once  settled,  as  the  same  sounds  will 
always  serve  to  excite  the  same  ideas  -9  if  he  can  but 


OF  LOGIC.  61 

contrive  to  register  his  words,  in  the  order  and  dispo- 
sition in  which  the  present  train  of  his  thoughts  pre- 
sents them  to  his  imagination  ;  it  is  evident  he  will  be 
able  to  recall  these  thoughts  at  pleasure,  and  that  too 
in  the  very  manner  of  their  first  appearance.  Accord- 
ingly we  find,  that  the  inventions  of  writing  and  paint- 
ing, by  enabling  us  to  fix  and  perpetuate  such  perish- 
able things  as  sounds,  have  also  furnished  us  with  the 
means,  of  giving  a  kind  of  permanency  to  the  transac- 
tions of  the  mind,  insomuch  that  they  may  be  in  the# 
same  manner  subjected  to  our  review,  as  any  the  other 
abiding  objects  of  nature. 

Sec.  II*. .,  And  of  the  mutual  Communication  of  Know* 
ledge  from  one  Man  te  another. 

But  besides  the  ability  of  recording  our  own  thoughts 
there  is  this  farther  advantage  in  the  use  of  external 
signs,  that  they  enable  us  to  communicate  our  senti- 
ments to  others,  and  also  receive  information  of  what 
passes  in  their  breasts.  For  any  number  of  men,  hav- 
ing agreed  to  establish  the  same  sounds  as  signs  of  the 
same  ideas,  it  is  apparent,  that  the  repetition  of  these 
sounds  must  excite  the  like  perceptions  in  each,  and 
create  a  perfect  correspondence  of  thoughts.  When 
for  instance,  any  train  of  ideas  succeed  one  another  in 
my  mind,  if  the  names,  by  which  I  am  wont  to  express 
them,  have  been  annexed  by  those  with  whom  I  con- 
verse, to  the  very  same  set  of  ideas,. nothing  is  more 
evident,  than  that  by  repeating  those  names,  according 
to  the  tenor  of  my  present  conceptions,  I  shall  raise  in 
their  minds  the  same  course  of  thought  as  has  taken 
possession  of  my  own.  Hence,  by  barely  attending  to 
what  passes  within  themselves,  they  wiH  also  become 
acquainted  with  the  ideas  in  my  own  understanding, 
and  have  them  in  a  manner  laid  before  their  view. 
So  that  we  here  clearly  perceive,  how  a  man  may  com- 
municate his  sentiments,  knowledge,  and  discoveries 
to  others,  if  the  .language  \n  which  he  converses,  be 
extensive  enough  to  mark  all  the  ideas  and  transactions 
of  his  mind.  But  as  this  is  not  always  the  case,  and 
»en  are  often  obliged  to  invent  tenns  of  their  own?  to 
F 


62  DUNCAN'S  ELEMENTS 

express  new  views  and  conceptions  of  thing ;  it  may  be 
asked,  how,  in  these  circumstances,  we  can  become  ac- 
quainted with  the  thoughts  of  another,  when  he  makes 
use  of  words  to  which  we  have  never  annexed  any  ideas, 
and  which  of  course,  can  raise  no  perceptions  in  our 
minds?  Now,  in  order*to  unveil  this  mystery,  and  give 
some  little  insight  into  the  foundation,  growth,  and 
improvement  of  language,  the  following  observations 
will  lam  apt  to  think,  be  found  of  considerable  moment. 

Sec.   III... •Simple  Ideas  cannot  be  conveyed  into    the 
Mind  by  Words,  or  a  Description  ; 

Tii*st,  that  no  word  can  be  to  any  man  the  sign  of  an 
idea,"~till  that  idea  comes  to  have  a  real  exigence  in  his 
mind.  For  names  being  only  so  far  intelligible,  as 
they  denote  known  internal  conceptions,  where  they 
have  none  such  to  answer  them,  there  they  are  plainly 
sounds  without  signification,  and  of  course  convey  no 
instruction  or  knowledge.  But  no  sooner  are  the  ideas 
to  which  they  belong  raised  in  the  understanding,  than, 
finding  it  easy  to  connect  them  with  the  established 
names,  we  can  join  in  any  agreement  of  this  kind  made 
by  others,  and  thereby  enjoy  the  benefit  made  by  their 
discoveries.  The  first  thing,  therefore,  to  be  consider- 
ed, is,  how  these  ideas  may  be  conveyed  into  the  mind  ; 
that,  being  there,  we  may  learn  to  connect  them  with 
their  appropriated  sounds,  and -so  become  capable  of 
understanding  others,  when  they  make  use  of  these 
sounds-ili  laying  open, and  communicating  their  tho'ts. 
Now  to  comprehend  this  distinctly  it  will  be  necessa- 
ry to  call  to  mind,  the  before-mentioned  divi-sion  of 
our  ideas  into  simple  and^  complex.  And  first,  as  for 
our  simple  ideas,  it  has  been  already  observed,  that 
they  can  find  no  admission  into  the  mind,  but  by  two 
original  fountains  of  knowledge,  sensation  and  reflex- 
ion. If  therefore  any  of  these  have  as  yet  no  being 
in  the  understanding,  it  is  impossible  by  words,  or  a 
description,  to  excite  them  there.  A  man,  who  had 
never  felt  the  impression  of  heat,  could  not  be  brought 
to  comprehend  that  sensation,  by  any  thing  we  might 
say  to  explain  it.     If  we  would  really  produce  the  ide* 


OF  LOGIC.  63 

in  him,  it  must  be  by  applying  the  proper  object  to  his 
senses,  and  bringing  him  within  the  inflrv.nce,  t>f-a,-h«>t 
body.  When  this  is  done,  and  experience  has  taught 
him  the  perception  to  traiefe  men  hive  m.iexel  the 
name,  keif*  it  then  becomes  to  him  the  sign  of  that' 
idea  ;  and  he  thenceforth  understands  the  meaning  of 
*.  term,  which,  before,  all  the  words  in  the  world  would 
not  have  been  sufficient  to  convey  into  his  mind.  The 
.case  is  the  same  in  respect  of  light  and  colours.  A  man 
born  blind,  .and  thereby  deprived  of  the  only  convey- 
ance for  the  ideas  of  this  class,  can  never  be  brought 
to  understand  the  names  by. which  they  are  expressed. 
The  reason  is  plain  ;  they  stand  for  ideas  that  have  no 
existence  m  his  mind  ;  and  as  the  organ  appropriated  to 
their  reception  is  wanting,  all  other  contrivances  are 
vain,  nor  can  they,  by  any  force  of  description,  be  rais- 
ed in  his  imagination.  But  it  is  quite  otherwise  in  our 
complex  notions.  For  these  being  no  more  than  cer- 
tain combinations  of  simple  ideas  put  together  in  va- 
rious forms — if  the  original  ideas,  out  of  which  these 
collections  are  made,  have  already  got  admission  into 
the  understanding,  and  the  names  serving  to  express 
them  are  known — it  will  be  easy,  by  enumerating  the 
several  ideas  concerned  in  the  composition,  and  mark- 
ing the  order  and  manner  in  which  they  are  united, 
to  raise  any  complex  conception  in  the  mind.  Thus 
the  idea  answering  to  the  word  rainbow^  may  be  readi- 
ly excited  in  the  imagination  of  another,  who  has  ne- 
ver seen  the  appearance  itself,  by  barely  describing  the 
figure,  largeness,  position,  and  order  of  colours;  if  we 
£.tppose  these  several  simple  ideas,  with  their  names, 
sufficiently  known  to  him. 

Sec.   IV. ...The  Nature  of  Complex  Ideas   Definable^ 
these  of  Simple  Ideas  not. 

And  this_  naturally  leads  me  to  a  second  observation, 
upon  this  s.ubject,  namely:  that  words  standing  for 
complex  ideas  are  all  definable';  but  these,  by'which 
we  denote  simple  ideas,  are  not.  For  the  perceptions 
of  this  latter  class,  having  no  other  entrance  into  the 
mind,  than  by  sensation  or  reflexion ;  can  only  be  ac- 


64  DUNCAN'S  ELEMENTS 

quired  by  experience  from  the  several  objects  of  nature* 
pops*-  to  prtDfl^-ce  those  perceptions  in  us.  Words, 
indeed,  may  very  well  serve  to  remind  us  of  them,  if 
they  have  already  found  admission  into  the  undetstand- 
ing,  and  their  connexion  with  the  established  names  is 
known  ;  but  they  can  never  give  them  their  original 
being  and  existence  there.  And  hence  it  is,  that  when 
anyone  asks  the  meaning  of  a  word  denoting  a  simple 
idea,  we  pretend  not  to  explain  it  to  him  by  a  defini- 
tion, well  knowing  that  to  be  impossible  ;  but  suppos- 
ing him  already  acquainted  with  the  idea,  and  only 
ignorant  of  the  name  by  which  it  is  called,  we  either 
mention  it  to  him  by  some  other  name,  with  which  we 
presume  he  knows  its  connexion,  or  appeal  to  the  ob- 
ject where  the  idea  itself  is  found..  Thus^  was  any  one 
to  ask  the  meaning  of  the  word  white,  we  should  tell 
him  it  stood  for  the  idea  as  albus,  in  Latin,  or  blanc,  in 
French;  or,  if  we  thought  him  a  stranger  to  these  lan- 
guages, might  appeal  to  an  object  producing  the  idea, 
by  saying,  it  denotedthe  colour  we  observe  in  snoiv  or 
milk.  But  this  is  by  no  means  a  definition  of  the  word, 
exiting  a  new  idea  in  his  understanding  ;  but  merely  a 
contrivance  to  remind  him  of  a  known  idea,  and  teach 
him  its  connexion  with  the  established  name.  For  if 
the  idea  after  which  he  enquires,  has  never  yet  been 
raised  in  his  mind- — as  suppose  one,  who  had  seen  no 
other  colours  than  black  andw/nJe,  should  ask  the  mean- 
ing of  the  word  scarlet — it  is  easy  to  perceive,  that  it 
would  be  no  more  possible  to  make  him  comprehend  it  by 
words,  or  a  definition,  than  to  inculcate  the  same  per- 
ception into  the  imagination  of  a  man  born  blind. 
The  only  method  in  this  case,  is,  to  present  some  ob- 
ject, by  looking  at  which  the  perception  itself  may  be 
excited  ;  and  thus  he  will  learn  both  the  name  and  the 
idea  together. 

Sec.  V .... Experience  and  Observation  bring  Men  to  ail 
Agreement  in  the  Names  of  Simple  Ideas. 

Should  any  one's  curiosity  now  prompt  him  to  enquire* 
how  it  comes  to  pass,  that  men  agree  in  their  names  of 
the  simple  ideas,   seeing  they  cannot  view  the  percep- 


OF  LOGIC.  6* 

tiotis  in  one  another's  minds,  nor  make  known  these 
perceptions  by  words  to  others  ;  I  answer,  that  the  ef- 
fect here  mentioned  is  produced  by  experience  and  ob- 
servation. Thus,  finding,  for  instance,  that  the  name, 
heat)  is  annexed  to  that  impression  which  men  feel 
when  they  approach  the  fire,  I  make  it  also  the  sign  of 
the  idea  excited  in  me  by;  such  an  approach,  nor  have 
any  doubt,  but  it  denotes  the  same  perception  in  my 
mind  as  in  their's.  For  we  are  naturally  led  to  ima- 
gine, that  the  same  objects  operate  alike  upon  the  or- 
gans of  the  human  body,  and  produce  an  uniformity  of 
sensations.  No  man  fancies,  that  the  idea  raised  in 
him  by  the  taste  of  sugar,  and  which  he  calls  sweet- 
ness, differs  from  that  excited  in  another  by  the  like 
means  ;  or  that  wormwood,  to  whose  relish  he  has  given 
the  ep'nhetbitter,  produces  in  others  the  sensation  which 
he  denotes  by  the  Word  sweet.  Presuming,  therefore, 
upon  this  conformity  of  perceptions,  when  they  arise 
from  the  same  objects,  we  easily  agree  as  to  the  names 
of  our  simple  ideas  ;  a*nd  if  at  any  time,  by  a  more 
narrow  scrutiny  into  things,  new  ideas  of  this  class 
come  in  our  way,  which  we  choose  to  express  by  terms 
of  our  own  invention  ;  these  names  are  explained  not 
by  a  definition,  but  by  referring  to  the  objects,  whence 
the  ideas  themselves  maybe  obtained. 

Sec.  VI.„,The  Conveyance  of  Complex  Ideas  by  Defi- 
nitions, a  wise  Contrivance  in  Nature  ; 

Being  in  this  manner  furnished  with  simple  ideas, 
and  the  names  by  which  they  are  expressed,  the  meaning 
of  terms  that  stand  for  complex  ideas  is  easily  attain- 
ed ;  because  the  ideas  themselves  answering  to  these 
terms,  may  be  conveyed  into  the  mind  by  definitions. 
For  our  complex  notions,  as  was  already  observed,  are 
only  certain  combinations  of  simple  ideas.  When, 
therefore,  these  are  enumerated,  and  the  manner  in 
which  they  are  united  into  one  conception  explained, 
nothing  more  is  wanting  to*  raise  that  conception  in  the 
understanding;  and  thus  the  term  denoting  it  comes 
of  course  to  be  understood.  And  here  it  is  worth  while, 
to  reflect  a  little  upon  the  wise  contrivance  of  nature, 

f  £ 


65  DUNCAN'S  ELEMENTS 

in  thus  furnishing  us  with  the  very  aptest  means  of 
communicating  our  thoughts.  For  were  it  not  so  or- 
dered, that  we  could  thus  convey  our  complex  ideas 
from  one  to  another  by  definitions,  it  would  in  many 
cases  be  impossible  to  make  them  known  at  all.  This 
is  apparent  in  those  ideas  Which  are  the  proper  work 
of  the  mind.  For  as  they  exist  only  in  the  understand- 
ing, and  have  no  real  objects  in  nature,  in  conformity 
to  which  they  are  framed, — if  we  could -not  make  them 
known  by  a  description,  they  must  lie  forever  hidden 
within  our  own  breasts,  and  be  confined  to  the  narrow 
acquaintance  of  a  single  mind.  All  the  fine  scenes,  that 
rise  from  time  to  time  in  the  poet's  fancy,  and,  by  his 
lively  painting,  give  such  entertainment  to  his  readers 
— were  he  destitute  of  this  faculty,  of  laying  them 
open  to  the  view  of  others  by  words  and  descriptions, 
— -could  not  extend  their  influence  beyond  his  own 
imagination,  or  give  joy  to  any  but  the  original 
inventor. 

Sec.  VII,, ..And  of  great   avail  towards  the  Improve- 
ment of  Knowledge, 

There  is  this  farther  advantage  in  the  ability  we  en- 
joy, of  communicating  our  complex  notions  by  defini- 
tions ;  that  as  these  make  by  far  the  largest  class  of  our 
ideas,  and  most  frequently  occur  in  the  progress  and 
improvement  of  knowledge  ;  so  they  are  by  this  means 
imparted  with  the  greatest  readiness,  than  which  no- 
thing could  tend  more  to  the  increase  and  spreading  of 
science.  For  a  definity  is  soon  perused,  and  if  the 
terms  of  it  are  well  understood,  the  idea  itself  finds  an 
easy  admission  into  the  mind.  Whereas  in  simple 
perceptions,  where  we  are  referred  to  the  objects  pro- 
ducing them,  if  these  cannot  be  come  at,  as  is  some- 
times the  case,  the  names,  by  which  they  are  expressed 
must  remain  empty  sounds.  But  new  ideas  of  this 
class  occurring  very  rarely  in  the  sciences,  •  they  sel- 
dom create  any  great  obstruction.  It  is  otherwise  with 
our  complex  notions  ;  for  every  step  we  take,  leading 
us  into  new  combinations  and  views  of  things,  it  be- 
comes necessary  to  explain  these  to  others,  before  they 


of  logic.  er 

can  be  made  acquainted  with  our  discoveries.  And  as 
the  manner  of  definitions,  is  easy,  requiring  no  appara- 
tus but  that  of  words,  which  are  always  ready,  and  at 
hand  ;  hence  we  can,  with  the  less  difficulty,  remove 
such  .obstacles,  as  might  arise  from  terms  of  our  own 
invention,  when  they  are  made  to  stand  for  new  com- 
plex ideas,  suggested  to  the  mind  by  some  present  train 
of  thinking.  And  thus  at  last  we  are  let  into  the  mys- 
tery hinted  at  in  the  beginning  of  this  chapter,  <viz» 
how  we  may  become  acquainted  with  the  thoughts  of 
another,  when  he  makes  use  of  words  to  which  we  have 
as  yet  joined  no  ideas.  The  answer  is  obvious,  from 
what  has  been  already  said.  If  the  terms  denote  simple 
perceptions,  he  must  refer  us  to  those  objects  of  nature, 
whence  the  perceptions  themselves  are  to  be  obtained  ; 
bat  if  they  stand  for  complex  ideas,  their  meaning  may 
be  explained  by  a  definition.  As  for  the  names  of  sim- 
ple ideas,  I  shall  here  dismiss  them  ;  it  being  sufficient 
to  take  notice,  that  our  knowledge  this  way  can  be  ex- 
tended only  by  experience  and  observation.  But  the 
theory  of  definitions  making  a  material  part  of  logic, 
and  being  indeed  of  great  importance  towards  the  im- 
provement of  human  knowledge,  it  will  be  necessary 
to  lay  it  a  little  more  open  to  the  view  of  the  reader. 

Sec.   VIII;... The  Composition  and  Resolution  of  our 
Complex  Ideas* 

Complex  ideas  are,  as  h?s  been  already  said,  no  other 
than  simple  ideas  put  together  in  various  forms.  But 
then  it  is  to  be  observed,  that  in  making  these  collec- 
tions, the  mind  is  not  always  tied  down  to  the  immedi- 
ate view  of  the  simple  perceptions  out  of  which  they  are 
framed.  For  if  we  suppose  the  understanding  already 
"furnished  with  a  considerable  stock  of  compound  no- 
tions, these  again  may  be  made  the  constituent  parts  of 
others  still  more  compounded,  insomuch  that  the  new 
idea  thence  arising  may  be  termed  a  combination  of 
complex  conceptions.  Thijs  the  idea  annexed  to  the 
word  animal,  includes  many  perceptions  under  it,  as 
life,  sense,  spontaneous  motion,  &c.  In  the  like  man- 
ner by  the  term  rational,  we  denote  a  variety  of  simple 


68  DUNCAN'S  ELEMENTS 

ideas.  If  now  combining  these  two  conceptions  toge- 
ther, we  form  the  still  more  complex  notion  of  a  ration- 
al animal;  the  idea  thus  got  is  truly  a  collection  of 
compound  notices.  In  a  word,  the  same  thing  happens 
here  as  in  numbers,  which  we  may  consider  not  only 
as  various  collections  of  units,  these  being  indeed  their 
original  and  constituent  parts;  but  also  as  sometimes 
composed  of  other  lesser  numbers,  which,  all  put  toge- 
ther, make  up  the  respective  sums.  Now  in  tracing 
any  very  large  number,  when,  for  the  ease  of  the  mind, 
we  consider  it  at  first  as  composed  of  various  others  still 
less — if  we  next  take,  these  less  parts,  to  pieces,  and 
pursue  them  continually,  until  we  arrive  at  the  units 
out  of  which  they  are  composed ;  we  thereby  totally 
unravel  the  collection,  and  being  able  to  push  our  re- 
searches no  farther,  rest  satisfied  in  the  view  thus  offered 
to  the  understanding.  Just  so  it  is  in  the  examination 
of  our  complex  ideas.  For  when  any  very  compounded 
notion  comes  under  the  inspection  of  the  mind,  in  or- 
der to  be  traced  to  its  first  principles — we  begin  with 
resolving  it  into  other  ideas  less  complicate'd;  and  taking 
these  again  to  pieces,  one  by  one,  still  go  on  with  the 
search,  until  we  have  broken  the  whole  into  our  first 
and  simple  perceptions,  beyond  which  the  pursuit  can- 
not possibly  be  carried.  And  this  is  the  reason  why  I 
have  all  along  called  our  simple  ideas  the  foundation 
and  groundwork  of  human  knowledge ;  because,  in 
unravelling  the  conceptions  of  the  mind,  we  find  our- 
selves at  length  bounded  by  these  ideas,  which  are  in- 
deed the  last  resort  of  the  understanding. 

Sec.  IX....77ze  Names  of  Simple  Ideas-may  be  consider- 
ed as  the  Elementary  Parts  Gf  Language. 

From  what  has  been  said,it  will  be  easy  to  conceive 
how,  in  defining  a  term,  standing  for  any  very  complex 
idea,  other  terms  may  be  introduced,  that  also  denote 
compound  ideas,  though  of  an  inferior  class.  For  the 
first  idea  being  resolvable  into  others  less  complicated  ; 
the  definition,  which  enumerates  these  component  ideas, 
must  consist  of  the  names  by  which  they  are  expressed. 
And  if  it  so  happen,  that  the  ideas  of  this  second  class 


OF  LOGIC.  65 

are  also  unknown,  their  terms,  too,  ought  to  be  still  far* 
ther  defined.  In  this  manner  may  a  series  of  definitions 
be  carried  on,  until  we  arrive  at  the  names  of  simple 
ideas,  which  not  being  definable,  the  analysis  must  ne- 
cessarily cease.  And  thus  we  see,  that  as  our  simple 
.  ideas  are  the  materials  and  foundation  of  knowledge,  so 
the  names  of  simple  ideas  may  be  considered  as  the  ele- 
mentary parts  of  language,  beyond  which  we  cannot 
trace  the  meaning  and  signification  of  words.  When 
we  come  to  them,  we  suppose  the  ideas  they  stand  for 
already  known ;  or,  if  they  are  riot,  experience  alone 
must^be  consulted',  and  not  definitions  or  explications. 
And  here  it  is  well  worth  our  notice,  that  as  the  names 
of  these  our  original  conceptions,  constitute  the  prima- 
tive  and  fnndamental  articles  of  speech,  upon  which 
the  whole  superstructure  of  human  language  is  built, 
so  they  are,  of  all  others,  the  least  doubtful  and  uncer- 
tain in  their  signification.  Because,  standing  each  for 
one  simple  perception,  not  precariously  excited  in  the 
mind,  but  the  effect  of  certain  powers  in  things,  fitted 
to  produce  that  sensation  in  us;  there  is  no  danger  of 
error  or  mistake.  He  that  once  knows  sweetness  to  be 
the  name  of  the  taste  received  from  sugar,  whiteness 
of  the  colour  in  snow  or  milk,  and  heat  of  the  sensation 
produced  by  approaching  the  fire,  will  not  be  apt  to 
misapply  those  words,  or  annex  them  to  perceptions  of 
a  different  kind.  And  as  the  names  of  complex  ideas 
may  all  be  resolved  into  these  primitive  terms,  it  is  ap- 
parent, that  we  are  sufficiently  provided  with  the  means 
of  communicating  our  thoughts  one  to  another ;  and 
that  the  mistakes  so  frequently  complained  of  on  this 
head,  are  wholly  owing  to  ourselves,  in  not  sufficiently 
defining  the  terms  we  use,  or  perhaps  not  connecting 
them  with  clear  and  determinate  ideas. 


70  DUNCAN'S  ELEMENTS 


Cfcap.  VI. 

OF  DEFINITION,  AND  ITS  SEVERAL 
KINDS. 

Sec,   I*,..  The  Variety  of  Definitions  proceeds  from  the 
various  Application  of  Words* 

HAVING  laid  these  foundations,  shown  what 
words  are,  and  what  are  not  definable,  and  taught 
.  the  manner  of  resolving  our  notions,  as  well  as  lan- 
guage itself,  into  its  first  and  original  principles  ;  we 
now  proceed  to  explain  a  little  more  particularly  the 
nature  of  a  definition,  and  the  several  kinds  made  use 
of,  according  to  the  different  views,  men  have  in  com- 
municating their  thoughts  one  to  another.  Definitions 
are  intended  to  make  known  the  meaning  of  words 
standing  for  complex  ideas  ;  and  were  we  always  care- 
ful to  form  those  ideas  exactly  in  our  minds,  and  copy 
our  definitions  from  that  appearance,  much  of  the  con- 
fu  ion  and  obscurity  complained  of  in  languages  might 
be  prevented.  But,  unhappily  for  us,  we  are  by  no 
means  steady  in  the  application  of  names,  referring 
them  sometimes  to  one  thing,  sometimes  to  another  ; 
■■which  often  creates  great  uncertainty  in  their  signifi- 
cation, and  obljges  us  to  give  a  different  turn  to  our  de- 
viations, according  to  the  different  reference  of  the 
terms  defined.  In  order,  therefore,  to  render  this 
whole  matter  as  clear  and  obvious  as  possible,  we  shall 
first  consider  to  what  it  is  that  names,  in  the  use  of 
language,  are  most  commonly  applied  ;  and  then  from 
the  variety  of  this  application,  endeavour  to  account 
for  the  several  methods  of  defining,  mentioned  in  the 
writings  of  logicians. 

Sec.  1L ...Words  have  a  threefold  Reference  ;  to  our 
own  Ideas,  those  of  others,  and  the  real  being  vf  things. 
Words  then  have  manifestly  a  threefold  reference. 
First,  and  more  immediately,  they  denote  the  ideas  in 
the  mind  of  him  who  uses  them;  and  this  is  their  true 
and  proper  signification.     When  a  man  speaks,   it  is 


OF  LOGIC.  71 

that  he  may  be  understood  ;  and  the  words  he  em- 
ploys to  convey  his  thoughts,  are  such  as  hy  use  he  has 
learned  to  connect  with  the  ideas  then  present  to  his 
mind.  But  because  those  with  whom  we  converse,  arc 
also  supposed-to  know  the  meaning  of  the  terms  we 
use,  hence,  secondly,  we  consider  our  words  as  signs, 
likewise,  of  the  ideas  in  their  n.inds  ;  and  this  is  the 
foundation  of  what  is  called  propriety  in  language, 
when  men  take  care  to  afrixsuch  notions  to  their  words, 
as  are  commonly  applied  to  them  by  those  of  most  un- 
derstanding in  l;he  country  where  they  live.  The  third 
and  last  reference  of  woi;ds  is  to  things  themselves. 
For  many  of  our  ideas  are  taken  from  the  several  ob- 
jects of  nature,  wherewith  we  arc  surrounded  ;  and. 
being  considered  as  copies  of  things  really  existing, 
the  words,  by  which  they  are  expressed,  are  often  trans- 
ferred frcm  the  ideas  themselves,  to  signify  those  ob- 
jects which  they  are  supposed  to  represent.  Thus  the 
word,  sun,  not  only  denotes  the  idea  excited  in  the 
1  by  that  sound,  but  is  also  frequently  made  to 
stand  for  the  luminous  body  itself,  which  inhabits  the 
centre  of  this  our  planetary  system.  Now,  according 
this  threefold  application  -of  names,  their- definitions, 
and  the  manner  of  explaining  them,  must  be  various  ; 
for  it  is  one  thing  to  unfold  the  ideas  in  a  man's 
own  mind,  another  to  describe  them,  as  they  are  sup- 
posed to  make  their  appearance  in  the  minds  of  others  ; 
and  lastly,  it  is  something  still  different,  to  draw 
images  or  pictures,  that  shall  carry  in  them  a  conform- 
ity to  the  being  and  reality  of  things.  But  we  shall 
treat  of  each  in  order. 

Sec.  III,.*. Definitions  of  the  Name  teach  only  the  Con- 
nexion of  our  Words  and  Ideas,  and  are  therefore 
arbitrary. 

First,  then,  when  we  consider  words,  as  signs  of  the 
ideas  in  the  mind  of  him  who  uses  them  ;  a  definition 
is  nothing  else,  but  such  an  explication  of  the  meaning 
of  any- term,  as  that  the  complex  idea  annexed  to  it  by 
the  speaker,  may  be  excited  in  the  understanding  of 
him  with  whom  he  converses,     And  this  is  plainly  uq 


72  DUNCAN'S  ELEMENTS 

Hi  ore  than  teaching   the   connexion,  of  our  words  and 
ideas,  that  others  may  understand  the  sense  of  our  ex- 
pressions, and  know  distinctly  what  notions  we  affix  to 
the  terms  we  use.     When  we  say,  for  instance,   that 
by  the  word  square  we  mean  a.  figure  bounded  by  four 
equal  sides,  joined  together  at   right  angles  ;    what  is 
this  but  a  declaration,  that  the- idea  of  a  quadrilateral, 
equilateral,  rectangular  figure,    is  that  which  in    dis- 
course or   writing  we  connect  with  the  term  square  ? 
This  is  that  kind  of  definition,   which   logicians    call 
the  definition   of  the  name  ;  because  it    discovers  the 
meaning  of  the  words   or  names   we  make  use  of,   by 
showing  the  ideas  for  which  they  stand.  Now,  as  sounds 
are  of  themselves  indifferent   to    signify   any   ideas, 
hence  it  is  plain,  that  the  definitions  of  names  are  arbi- 
trary, every  man  having  a  liberty  to  affix  what  notions 
he  pleases  to  his  words.     But  the  convenience  of  com- 
munication making  it  necessary  for  men  speaking   the 
same  language  to  agree  as  nearly  as  possible  in  the  sig- 
nification of  sounds,  a  conformity  has  accordingly  been 
studied.     Nevertheless,    we  find  that  differences  will 
from  time  to  time  creep  in,   which  must  create  great 
confusion  in  men's  discourses  and  reasonings,    if  they 
are  not  careful  to  define  their  terms,  that  their  signifi- 
cation  may   be  kept  fixed  and   steady,  and  lie  always 
open  to  the  view  of  the  mind*    The  writings   of  the 
mathematicians  are  a  clear  proof,  how  much  the  ad- 
vancement of  human  knowledge  depends  upon  a  right 
use  of  definitions.     For    as    by   means  of   them  they 
every  where  preserve   the    same   determined  significa- 
tion to  their  words,  hence  there  is  little  dispute  as   to 
the  meaning  of  their  expressions,    almost  all  men  un- 
derstanding them  in  the  same  sense.  And  thus  it  hap- 
pens, that  such  as  apply  their  thoughts  this  way,  hav- 
ing perfectly  the  same  views  of  things,  readily  compre- 
hend the  discoveries  already  made,  and  are  thereby  ena- 
bled with  joint  labour,  and  an  exact  conformity  of  no- 
tions, to  carry  on  the   improvement  of  this  branch  of 
knowledge.      And    if    men  in  other  parts  of  learning, 
were  alike  careful  to  fix  the  meaning    of  their  terms, 
the  progress  of  science  must  be  greatly  furthered,  and 


OF  LOGIC.  73 

all  those  verbal  disputes,  that  now  so  much  interrupt 
the  course  of  our  improvement,  might  be  prevented. 

Sec.  IV. ...Definitions   of   the  Name  not  always   true 
and  real  Definitions  ; 

This  then  ought  to  be  our  first  care,  when  we  enter 
upon  a  design  of  illustrating  any  particular  branch  of 
study;  to  ascertain  our  ideas,  and  mark  the  names  by 
which  they  are  expressed.  And  although  definitions  of 
words  are  indeed  arbitrary,  (for  a  man  may  affix  what 
ideas  he  pleases  to  his  terms,  nor  can  any  one  contest 
this  liberty  with  him,)  yet  it  will  be  proper  to  conform, 
as  near  as  possible,  to  common  acceptation,  that  there- 
by our  thoughts  may  find  a  more  easy  and  ready  en- 
trance into  the  minds  of  others.  If  it  should  now  be 
asked,  what  are  the  rules  of  a  good  definition;  I  an- 
swer, that  as  in  definitions  of  the  name,  we  aim  at  no 
more  than  teaching  the  connexion  of  words  and  ideas; 
every  contrivance,  by  which  we  are  enabled  to  excite 
the  idea  annexed  to  any  word  in  the  mind  of  another, 
will  serve  the  purpose  of  a  definition.  Now  the  ideas 
we  join  with  our  words  are  of  two  kinds:  either  such 
as  we  have  reason  to  believe  are  already  in  the  minds  of 
others,  though  perhaps  they  know  not  the  names  by 
which  they  are  called  ;  or  such  as,  being  new  and  of  our 
own  formation,  can  be  no  otherwise  made  known  than 
by  a  description.  In  the  first  case,  there  is  no  necessi- 
ty for  laying  open  the  idea  itself,  because  being  already 
known,  any  contrivance  to  remind  us  of  it  is  sufficient. 
When  we  say  for  instance,  that  a  clt  ck  is  an  instrument^ 
by  which  we  measure  the  hours  of  the  day  ;  it  is  plain, 
that  the  idea  answering  to  the  word  clock,  is  not  here 
unfolded ;  but  we  being  before-hand  supposed  to  have 
an  idea  of  this  instrument,  are  only  taught  by  what 
name  it  is  called.  Now  in  this  sense,  the  names  of 
even  simple  ideas  may  be  defined.  For,  by  saying  that 
ivhite  is  the  colour  we  observe  in  snow  or  milk,  heat 
the  sensation  produced  by  approaching  the  fire,  we  suf- 
ficiently make  known  what  ideas  we  connect  with  the 
terms,  white  and  heat,  which  is  the  true  purpose  of  a 
definition  of  the  name.     Hence  it  appears,  that  many 


74  DUNCAN'S  ELEMENTS 

of  those  explanations  of  words,  which  logicians  call  de- 
finitions of  the  name,  are  not  definitions  in  a  true  and 
proper  sense,  that  is,  such  descriptions  of  ideas,  as 
•would  serve  to  excite  them  in  the  mind  of  another,  even 
supposing  him  before  wholly  unacquainted  with  them, 
but  merely  contrivances  to  remind  us  of  known  ideas, 
and  teach  us  the  names  by  which  they  are  called. 
Sec,  Y,,,,But  only  when  they  Coincide  with  the  Defi- 
nition of  the  Thing, 
But  where  the  ideas  we  join  with  our  words,  are  new 
and  of  our  own  formation,  there  they  are  to  be  laid  open 
by  a  description,  because,  being  supposed  unknown  to 
others,  we  must  first  raise  them  in  their  minds,  before 
they  can  learn  to  connect  them-  with  any  particular 
names.  And  here  it  is,  that  the  definition  of  the  name 
coincides  with  what  logicians  call,  the  definition  of  the 
thing,  as  in  either  case  we  proceed  by  unfolding  the 
idea  itself  for  which  the  term  defined  stands.  And 
indeed  this  alone  is  what  constitutes  a  definition,  in 
the  true  and  proper  sense  of  the  word,  as  will  appear 
more  fully  afterwards,  when  we  come  to  consider  the 
terms  we  use,  as  referred  to  the  real  objects  of  nature. 
We  shall  therefore  postpone  this  consideration  of  the 
definition  of  the  name,  till  we  come  to  treat  of  the  de- 
finition of  the  thing,  when  it  will  more  naturally  fall 
in  our  way.  It  may  not,  however,  be  amiss  to  observe, 
that  when  we  say  the  definitions  of  the  name  are  arbi- 
trary, we  mean  not  that  the  descriptions  of  ideas  are 
so  too.  For  every  idea  having  a  peculiar  appearance 
of  its  own,  by  which  it  is  distinguished  from  all  others, 
nothing  is  more  evident,  than  that  the  description  must 
be  such  as  to  exhibit  that  precise  conception.  But 
then  the  connexion  of  any  idea,  with  the  name  by 
which  it  is  expressed,  being,  as  we  have  said,  wholly 
arbitrary,  the  considering  the  description  of  that  idea 
as  the  definition  of  that  particular  name  rqust  be  so  too. 
So  that  although  definitions,  considered  as  descriptions 
of  our  ideas,  are  steady  and  invariable,  yet  the  appli- 
cation of  them  to  particular  sounds,  (which  is  ail  that 
we  understand  by  the  definition  of  the  name)  is  wholly 
a  work  Qf  our  own  free  choice. 


OF  LOGIC.  YS 

Sec.  VI.... Definition  of  IVords  according  to  the  com* 
mon  use  of  Language  nut  Arbitrary. 

But  secondly,  besides  considering  words  as  the  signs 
of  our  own  ideas,  we  arc  also  very  apt,  on  many  occa- 
sions, to  refer  them  to  the  ideas  in  the  minds  of  other 
men.  Now,  to  define  a  term,  in  this  view,  is  to  inves- 
tigate its  meaning  or  acceptation,  according  to  the 
common  use  of  speech.  Here  then  it  is  plain,  that  de- 
finitions are  not  arbitrary.  For  although  in  regarding 
words  as  the  marks  of  our  own  ideas,,  we  may  give  them 
what  meaning  we  please;  yet  when  we  consider  them 
in  reference  to  the  thoughts  of  others,  they  have  a  fix- 
ed and  steady  signification  ;  namely,  that  which  custom 
and  the  propriety  of  languagAas  assigned  them.  The 
words,  ability  and  genius,  may,  by  any  man,  be  made? 
to  stand  for  one  and  the  same  idea  in  his  own  mind, 
and  if  he  takes  care  to  advertise  us  of  this,  he  is  at  IU 
berty  to  use  them  promiscuously.  But  if  the  common 
course  of  language  hath  confined  the  word  genius  to 
express  the  natural  strength  and  talents  of  the  mind, 
and  the  word  ability  to  denote  those  which  are  acquir- 
ed, whoever  pretends  to  explain  the  proper  acceptation 
of  these  terms,  is  bound  to  take  notice  of  this  differ-* 
ence.  As  propriety  of  speech  makes  our  language  in- 
telligible, and  gives  our  thoughts  a  ready  entrance  into 
the  minds  of  others,  it  well  deserves  our  application  and 
care.  The  best  way  to  acquire  it  is  from  the  writ- 
ings and  discourses  of  those  who  seem  to  have  had  the 
clearest  notions,  and  to  have  applied  their  terms  with 
the  exactest  choice  and  fitness. 

Sec.  V "II.. ..Definitions  of  the  Thing  refer  to  the  real 
Objects  of  Nature. 
We  come  now  to  the  third  and  last  species  of  defini- 
tion, that  namely,  which  considers  words  as  referred  to 
things  themselves.  And  here  it  is  plain,  we  are  not  at 
liberty  to  feign  and  fashion  our  explications  at  pleasure, 
but  being  tied  down  to  the  real  objects  of  nature  must 
study  a  conformity  to  things  themselves.  When  we 
define,  for  instance,  the  sun,  considered  as  that  being 
who  possesses  the  centre  of  our  system,  and  diffuses 


76  DUNCAN'S  ELEMENTS 

heat  and  light  to  the  planets  around  him  ;  it  is  not 
enough  that  we  give  an -account  of  the  idea,  answer- 
ing to  that  word  in  our  minds.  We  must  further 
take  care,  that  the  idea  itself  carries  in  it  a  real-con- 
formity to  the  object  it  is  supposed  to  represent.  And 
hence  it  is,  that  all  definitions  of  this  kind,  when  just- 
ly made,  are  in- reality  pictures  or  representations,  ta- 
ken from  the  being  and  existence  of  things.  For  they  - 
are  intended  to  express  their  nature  and  properties  so 
as  to  distinguish  them  from  all  others,  and  exhibit 
them  clearly  to  the  view  of  the  mind.  *Tis  for  this 
reason-  that  logicians  call  them  definitions  of  things,, 
because  they  are  supposed  to  refer,  not  so  much  to  the 
ideas  in  the  understanding,  as  to  the  things  themselves 
represented  by  those  ideas. 

Sec.  VIII... .Ground  of  the  distinction  between  the  de- 
finition of  the  Name  and  of  the  Thing. 

And  this  also  lets  us  into  the  ground  of  that  distinc- 
tion so  universally  received  between  definitions  of  the 
name  and  of, the  thing.  The  first  are  arbitrary,  and 
not  liable  to  debate  or  contradiction.  The  second  are 
propositions,  capable  of  proof  and  illustration,  and 
which  may  therefore  be  contested.  The  reason  is  ob- 
vious. Definitions  of  the  name  serve  only  to  mark  what 
ideas  we  connect  with  our  words.  And  as  sounds  are 
of  themselves  indifferent  to  signify  any  ideas,  we  are  en- 
tirely at  liberty  to  affix  to  them  what  notions  we  please. 
But  it  is  otherwise  in  the  definition  of  the  thing.  For 
here  our  words,  serving  to  denote  particular  beings  in 
nature,  cannot  be'  the  signs  of  any  ideas  at  pleasure,  but 
of  such  only  as  carry  in  them  a  conformity  to  the  sever- 
al objects  to  which  the  words  refer.  A  man  may  use 
the  term,  square,  to  express  that  idea,  which  others  de- 
note by  the  word,  triangle,  and  define  it  accordingly* 
In  this  case,  indeed,  he  recedes  from  the  common  forms 
of  speech,  but  his  definition  cannot  be  charged  with 
falsehood.  Fie  tells  us  that  by  a  square  he  means  a 
three-sided  figure ;  and  who  can  dispute  the  truth  of 
this,  if  he  really  all  along  uses  the  word  in  that  sense  ? 
I  would  only  observe,  that  by  changing  thus  the  mea^ 


OF  LOGIC.  77 

ing  of  words,  we  change  not  things  themselves,  or  their 
relations  and  habitudes  one  towards  another.  These 
are  at  all  times  the  same  and  invariable,  nor  have  any  de- 
pendence upon  the  fancy  and  caprice  of  men.  It  is  true, 
the  properties  of  the  triangle  may,  after  this  definition, 
be  affirmed  of  the  square  ;  but  as  in  either  case,  the  idea 
to  which  these  properties  belong,  is  the  same,  the  pro- 
positions  only  expressing  our  judgments,  and  not  our 
judgments  themselves,  suffer  a  seeming  variation. 

Sec.  IX. *;A  previous  connexion  between  Names  and 
Things,  cuts  off  all  Arbitrary  Explications. 
But  where  words  are  made  to  denote  particular  ob- 
jects, previous  to  any  definitions  given,  there  arbitrary- 
explications  cannot  have  place.  For  in  this  case,  we 
are  not  put  upon  explaining  what  ideas  we  connect  with 
our  words,  but  a  connexion  being  already  supposed  be- 
tween  the  name  and  the  thing  signified,  our  "business 
is  to  unfold  that  idea  by  which  the  object  itself  is  most 
clearly  and  distinctly  represented.  Thus  the  word  gold 
denotes  that  metal  which  is  of  highest  value  among  men, 
and  goes  farthest  in  the  way  of  commerce.  This  con- 
nexion being  once  settled,  we  are  no  longer  left  to  ar- 
bitrary definitions,  but  must  describe  it  by  such  proper- 
ties as  are  really  to  be  fou.nd  in  it,  and  will  best  serve  to 
distinguish  it  when  it  comes  in  our  way ;  as  by  saying  it 
is  a  substance  yellow,  very  heavy,  malleable, fusible,  Sec. 

Sec.  X...jr/jv  Mathematical  Definit ions  have  been  ac- 
counted mere  Dejinitions  of  the  Name  ; 
From  what  has  been  said,  it  appears,  that  in  the  lan- 
guage of  logicians,  definitions  of  the  thing  respect  only 
substances  and  beings  that  have  a  real  existence  m  na- 
ture, serving  to  describe  them  by  their  properties  and 
attributes.  And  this,  I  doubt  not,  is  the  reason,  that 
the  definitions  of  the  mathematicians  are  not  consider*- 
ed  as  definitions  of  the  thing,  but  of  the  name  ;  because 
the  ideas  therein  described,  are  the  mere  creatures  of 
the  understanding,  and  not  supposed  to  be  copied  from 
patterns  existing  without  us.  A  circle,  a  triangle,  a 
square,  &c.  such  as  mathematicians  conceive  them,  are 
no  where  to  be  found  in  nature,  that  we  know  of* 


73  DUNCAN'S  ELEMENTS 

Hence  it  might  justly  be  accounted  absurd,  to  call  our 
definitions  of  these,  definitions  of  the  thing,  when  they 
serve  not  to  describe"  any  real  objects  of  nature,  but 
merely  to  unfold  the  conceptions  of  the  mind.  And 
yet  if  we  look  into  the  matter  narrowly,  we  shall  find, 
that  the  rules  followed  in  these  definitions  are  precisely 
the  same  with  those  which  logicians  have  laid  down 
for  the  definition  of  the  thing.  All  the  several  species 
of  figures  are  described  by  their  properties,  some  of 
•  which  are  common  to  different  ranks,  others  peculiar 
to  the  tribe  defined.  The  common  properties  consti- 
tute what  logicians  call  the  genus,  and  those  that  are 
peculiar,  the  difference.  Now  the  genus  and  differ- 
ence make  up  the  logical  definition  of  the  thing,  as  will 
be  more  clearly  understood  from  what  follows* 

Sec.  XI.  When  yet  they  coincide  with  the  logical  defi* 
nition  of  the  thing,  and  therefor*  ought  not  to  be  ac- 
counted arbitrary* 

I  am  therefore,  apt  to  think,  that  mathematical 
definitions,  as  they  are  of  the  same  general  with  the 
definitions  of  substances,  and  subject  to  the  same  rules, 
have  been  improperly  considered  as  mere  definitions  of 
the  name,  m  which  we  are  left  wholly  to  arbitrary 
explications.  For  however  we  may  change  the  name 
of  one  figure  for  another  in  discourse  or  writing,  using 
the  term  square  to  denote  a  triangle,  or  the  word  tri- 
angle to  express  a  square,  it  is  certain  the  ideas  them- 
selves are  invariable,  and  no  less  capable  of  being 
distinguished  by  their  properties,  than  the  several  spe- 
cies of  substances.  Thus  if  we  suppose  the  word 
square  to  denote  that  species  of  figures,  whose  sides 
severally  subtend  quadrants  of  a  circumscribed  circle, 
we  shall  find  ourselves  equally  shut  out  from  arbitrary 
explications,  as  in  the  definition  of  the  names  of  sub- 
stances. For  as  this  happens  in  no  figures  but  those 
which  are  bounded  by  four  equal  sides  joined  together 
at  right  angles  ;  it  follows  evidently,  that  the  true  and 
proper  definition  of  a  square,  is  that  which  exhibits 
the  precise  idea  here  mentioned,  and  no  other,  to  the 
mind,  And  thus  it  appears,  that  the  common  drvisicn 


OF  LOGIC,  n 

of  definitions,  into  those  of  the  name  and  thing,  is  not 
sufficiently  calculated  to  give  us  right  apprehensions, 
as  to  what  is  and  what  is  not  arbitrary  in  the  explica- 
tion of  words.  It  may  not,  therefore,  be  improper,  if 
we  here  endeavour  to  clear  up  this  matter  a  little,  and 
free  it  from  those  obscurities  in  which  it  has  hitherto 
been  involved.  To  this  end  we  shall  premise  the  foL 
lowing  observations. 

Sec.  XII... . Definitions, property  speaking,  never  regard 
Things,   but  merely  our  own  Ideas. 

1.  First,  that  whatever  logicians  may  pretend  about 
the  definition  of  the  thing,  it  is  yet  certain,  that  none 
of  our  definitions,  when  pursued  to  their  source,  regard 
immediately  things  themselves,  but  merely  the  ideas 
in  our  own  minds.  This,  I  doubt  not,  will  appear  a 
paradox  to  many,  who  will  be  apt  to  enquire,  whether 
the  definition  of  gold,  be  not  taken  from  that  metal, 
independent  of  the  various  conceptions  of  men  about 
it.  To  this  I  answer,  that  indeed  in  framing  our  idea 
of  gold,  we  regard  chiefly  the  thing  itself,  uniting  in 
our  conception  such  properties  as  are  most  conspicuous, 
and  serve  best  to  distinguish  it  from  other  metals,  to 
which  it  may  bear  any  resemblance.  But  as  it  is  by  this 
idea  alone  that  gold  is  known  to  us,  so  in  describing  it 
to  others,  we  aim  at  nothing  more  than  to  transfer  the 
same  conception  into  their  minds.  Now  this  can  no 
otherwise  be  done,  but  by  enumerating  the  several  pro- 
perties of  which  our  own  complex  notion  is  formed. 
And  indeed  it  were  in  the  highest  degree  absurd  to  ima- 
gine, that  men  in  explaining  things  to  others,  should 
make  use  of  any  marks  or  characters  but  those  by  which 
they  are  known  to  themselves.  Hence  it  comes  to  pass, 
that  all  our  definitions  are  in  fact  nothing  else  but  tran- 
scripts of  the  ideas  in  our  minds.  Where  these  are  im- 
perfect, the  definitions  must  be  so  too  ;  where  they  are 
just  and  adequate,  the  copies  taken  from  them,  if  drawn 
out  with  accuracy  and  care,  cannot  fail  to  exhibit  the 
©bject  described.  And  this  will  very  well  serve  to  ac- 
count for  that  great  diversity  of  definitions  we  often 
inect  with,  even  of  one  and  the  same  object.     Because 


80  DUNCAN'S  ELEMENTS 

men,  in  consequence  of  their  different  pursuits  and  ap- 
plications, falling  often  into  different  views  of  things, 
must  needs  vary  no  less  in  their  definitions,  than  in  the 
ideas  themselves  from  which  these  definitions  are  copi- 
ed.     He,  whose  observation  goes  no  farther  than  the 
more  obvieus  qualities  of  gold,   will   content    himself 
with  describing  it  by  its  colour,   weight,    and  perhaps 
malleability  and   fusibility.      On    the    other    hand,    a 
goldsmith,   having  enquired   farther   into   the    nature 
ef  that  metal,  and  finding  several  other  properties  that 
equally  belongs  to  it,  will  be  apt  to  take  these  also  into 
his  complex  idea,  and  accordingly  introduce  them  in  a 
definition.    Hence  his  description  will  add  to  the  form- 
er, fixedness,  and  solubility  in  aqua  regia,  Sec.    And  so 
in  proportion,  as  men's  various  pursuits  lead  them  into 
a  more  accurate  examination  of  things,  their  explica- 
tions will  take  a  different  turn,   suitable  to  the  ideas 
they  have  framed  within  themselves. 
Sec.  XIII..... Distinction  between  the  Definition  of  the 
name  and  thing  useless,  and  to  be  rejected. 
2.  This  then  being  evident,  that  our  definitions  re- 
spect not  things  themselves,  but  the  ideas  in  our  own 
minds ;    I  would  in  the  next  place  observe,  that  the  dis- 
tinction of  them  into  those  of  the  name  and  thing,  is 
altogether  useless,  and  tends  rather  to  mislead  us  than 
give  right  apprehensions  of  the  subject  in  hand.     For 
thus  men  are  apt  to  fancy,  that  many  of  their  defini- 
tions are  expressive  of  the  real  essence  of  things,  where- 
as they  are  in  truth  no  more  than  transcripts  of  their 
own  ideas.     And'as  it  sometimes  falls  out,  that  these 
ideas;  are  not  collected  with  sufficient  care,   from  the 
objects  they  represent  ;    we  find,  by  experience,  that  a 
mistaken  idea  never  fails  to  occasion  a  mistake  also  in 
the  definition.      But  this   could  not  happen,  were  our 
definitions  copied  from  things  themselves  :  because  their 
essences  being  immutable  and  always  the  same,  the  defi- 
nition would  in  thi?  case  sejve  to  correct  the  idea,  and 
might  be  considered  as  a  standard,  by  which  to  judge 
whether  the  idea  was  rightly  framed.     I  deny  not,  that 
words  are  often  transferred  from  our  ideas  to  signify  the 
objects  which  these  ideas  represent  j   as  whea  we  talk 


OF  LOGIC,  81 

of  the  sun,  the  earth,  men,  and  other  animals.  But 
then  let  it  be  observed,  that  as  these  objects  are  only 
known  to  us,  by  the  ideas  of  them  in  our  minds  ;  so,  in 
describing  them  to  others,  all  we  aim  at  is,  distinctly, 
to  lay  open  our  conceptions  about  them.  Hence  it 
appears,  that  what  logicians  call  a  definition  of  the 
thing,  is  in  truth  no  more  than  an  unfolding  of  the 
idea,  by  which  that  thing  is  represented  to  the  under- 
standing. But  now  in  mathematical  definitions,  and  in- 
deed all  others  whatsoever,  this  also  is  our  whole  aim  and 
intent,  to  exhibit  and  lay  open  those  ideas,  of  which 
the  words  we  use  are  the  signs.  And  thus  it  happens, 
that  in  innumerable  instances,  what  logicians  call  the 
definition  of  the  name,  is  yet  found  to  coincide  with 
and  proceed  by  the  very  same  rules,  as  the  definition  of 
the  thing;  which  clearly  demonstrates  the  necessity  of 
banishing  this  frivolous  distinction,  and  establishing 
some  precise  and  determinate  notion,  expressive  of  the 
true  nature  of  a  definition,  and  comprehending  it  in  its 
full  extent 

Sec.  XIV Definitions  in  all  cases  descriptions  of 

our  Ideas. 

Nor  will  this  appear  so  difficult  a  task,  if  we  call  to 
mind,  that  words  are  in  all  cases  the  signs  of  our  ideas* 
and  no  otherwise  signify  things,  than  as  they  stand 
for  those  ideas  by  which  things  are  represented  to  the 
understanding.  By  defining  our  words,  therefore,  we 
can  mean  no  more,  than  the  laying  open  to  the  view 
of  others,  the  ideas  of  which  these  words  are  the  signs» 
For  thus  it  is,  that  the  meaning  of  our  expressions 
comes  to  be  known,  and  that  we  find  ourselves  capable 
of  tran?£erring  our  thoughts  and  conceptions  into  the 
minds  of  those  with  whom  we  converse.  Where  words 
are  referred  to  things  themselves,  there  we  explain  the 
ideas  by  which  these  things  are  represented  ;  where 
they  denote  conceptions  framed  by  the  mind,  there  we 
lay  open  these  conceptions,  and  endeavour  to  exhibit 
them  according  to  their  real  appearance  within  our 
own  breasts.  But  in  both  cases,  it  is  our  own  ideas, 
it  is  the  perceptions  of  our  own  minds,  either  as  taken 


B2  DUNCAN'S  ELEMENTS 

from  things  without,  or  framed  by  the  understanding 
itself,  that  we  explicate  an4  unfold. 

Sec.  XV Not  arbitrary ,    as    being   confined  to  ths 

Representation  of  certain  determinate  Notions* 
And  thus  we  have  at  length  settled  the  true  and  ge- 
nuine notion  of  a  definition,  comprehending  all  its  va- 
rieties, from  whatever  science  taken,  or  to  whatever 
object  extended.  For  from  what  we  have  said,  it  evi- 
dently follows,  that  a  definition  is  the  unfolding  cf 
some  conception  of  the  mind,  answering  to  the  word  cr 
term  made  use  of  as  the  sign  of  it.  Now,  as  in  exhi- 
biting any  idea  to  another,  it  is  necessary  that  the  de- 
scription be  such  as  may  excite  that  precise  idea  in 
his  mind  ;  hence  it  is  plain,  that  definitions,  proper- 
ly speaking,  are  not  arbitrary,  but  confined  to  the  re- 
presenting of  certain  determinate  settled  notions,  such, 
namely,  as  are  annexed  by  the  speaker  or  writer  to 
the  words  he  uses.  As,  nevertheless,  it  is  universally- 
allowed,  that  the  signification  of  words  is  perfectly  vo- 
luntary, and  not  the  effect  of  any  natural  and  necessary 
connexion  between  them  and  the  ideas  for  which  ihey 
stand,  some  may  perhaps  wonder  why  definitions  are 
not  so  too.  In  order,  therefore,  to  unravel  this  diffi- 
culty, and  show  distinctly  what  is,  and  what  is  not  ar- 
bitrary in  speech  wre  must  carefully  distinguish  be- 
tween the  connexion  of  our  words  and  ideas,  and  the 
unfolding  of  the   ideas  themselves. 

Sec.  XVI The  Connexion  between  Words  andldeasf 

a  perfectly  voluntary  Establishment* 
First,  as  to  the  connexion  of  our  words  and  ideas, 
this,  it  is  plain,  is  a  purely  arbitrary  institution.  When 
for  instance,  we  have  in  our  minds,  the  icea  of  any 
particular  species  of  metals,  the  calling  it  by  the  name 
goldy  is  an  effect  of  the  voluntary  choice  of  men  speak- 
ing t,he  same  language,  and  not  of  any  peculiar  apt- 
ness in  that  sound  ,to  express  that  idea.  Other  nations, 
we  find  make  use  of  different  sounds,  and  .with  the 
same  effect.  Thus  aurum  denotes  that  idea  in  Latin, 
and  or  in  French.  And  even  the  word  gold  itself, 
would  have  as  well  served  to  express  the  idea  of  that 


OF  LOGIC.  83 

metal  which  we  call  silver,   had  custom  in  the  begin- 
ning so  established  it. 

Sec.  XVII.....  TAj?  Descriptions  of  Ideas  not  so,  but 
bounded  to  the  Representation  of  that  precise  xip- 
pearance  by  which  they  are  distinguished  among 
themselves. 

But  although  we  are  thus  entirely  at  liberty,  in 
connecting  any  idea  with  any  sound,  yet  it  is  quite 
otherwise  in  unfolding  the  ideas  themselves.  For  eve- 
ry idea,  having  a  precise  appearance  of  its  own,  by 
•which  it  is  distinguished  from  every  other  idea  ;  it  is 
manifest,  that  in  laying  it  open  to  others,  we  must 
study  such  a  description,  as  shall  exhibit  that  peculiar 
appearance.  When  we  have  formed  to  ourselves  the 
idea  of  a  figure  bounded  by  four  equal  sides,  joined  to- 
gether at  right  angles,  we  are  at  liberty  to  express  that 
idea  by  any  sound,  and  may  call  it  either  a  square  or  a 
triangle.  But  which  ever  of  these  names  we  use,  so 
long  as  the  idea  is  the  same,  the  description,  by  which 
we  would  signify  it  to  another,  must  be  so  too.  Let 
it  be  called  square  or  triangle,  it  is  still  a  figure  hav- 
ing four  equal  sides,  and  all  its  angles  right  ones. 
Hence  we  clearly  see,  what  is,  and  what  is  not  arbitary 
in  the  use  of  words.  The  establishing  any  sound,  as 
the  mark  of  some  determinate  idea  in  the  mind,  is  the 
effect  of  free  choice,  and  a  voluntary  combination  a- 
mong  men.  And  as  different  nations  make  use  of 
different  sounds,  to  denote  the  same  ideas,  hence  pro- 
ceeds all  that  variety  of  languages  which  we  meet  with 
in  the  world.  But  when  a  connexion  between  our 
ideas  and  words  is  once  settled,  the  unfolding  of  the 
idea  answering  to  any  word,  which  properly  consti- 
tutes a  definition,  is  by  no  means  an  arbitrary  thing. 
For  here,_as  I  have  already  observed,  we  are  bound  to 
exhibit  that  precise  conception,  which  either  the  u%% 
of  language  or  our  own  particular  choice,  hath  annex- 
ed to  the  term  we  use. 


84  DUNCAN'S  ELEMENTS 

Sec.  XVIII Causes  of  the  Obscurity  that  has  hither* 

to  perplexed  the  Iheory  of  Definitions, 

And  thus  it  appears,   that  definitions,  considered  as 
descriptions  of  ideas  in  the  mind,  are  steady  and  inva- 
riable,  being  bounded  to  the  representation   of  those 
precise  ideas.  But  then  in  the  application  of  definitions 
to  particular  names,  we  are  altogether  left  to  our  own 
free  choice.     Because  as  the  connecting  of  any   idea 
with   any   sound,  is  a  perfectly  arbitrary  institution  ; 
the    applying  the    description   of  that  idea,    to    that 
sound,  must  be  so  too.   When,  therefore,  logicians  tell 
us,  that  the  definition- of   the  name   is  arbitrary,  they 
mean   no  more  than  this  ;  that  as  different  ideas  may 
be    connected  with  any  term,  according  to    the    good 
pleasure  of  him  that  uses  it,  in  like  manner  may  differ- 
ent   descriptions  be  applied  to  that  term,    suitable    to 
the  ideas  so  connected.  But  this  connection  being  set- 
tled, and  the  term  considered  as  the  sign  of  some  fixed 
idea  in  the  understanding,  we  are  no  longer  left  to  ar^ 
bitrary    explications,  but  must   study  such  a  descript- 
ion as  corresponds  with  that  precise  idea.     Now  this 
alone,   according  to  what   has  been  before  laid  down, 
ought  to  be   accounted  a  definition.     What,  I  am  apt 
to  think,    has  occasioned  no  small,  confusion   in    this 
matter  is,  that  many  explanations  of  words,  where  no 
idea  is    unfolded,   but  merely  the  connexion  between 
some  word  and  idea  asserted,   have  yet  been  dignified 
with  the  name   of  definitions.     Thus,  in -the  instance 
before   given,  when  we  say  that  a  clock   is  an  instru- 
ment by  which  we  measure  time  ;  this  is  by  some  called 
a   definition.     And  yet  it  is  plain,  that  vve  are  before*, 
hand  supposed  to  have  an  idea  of  this  instrument,  and 
only  taught  that  the  word,  clocks    serves   in   common 
language  to  denote  that  idea.      By  this  rule  all  expli- 
cations of  words  in  our  dictionaries  will  be  definitions  ; 
nay,  as  was  already  observed,  the  names  of  even  sim- 
ple ideas  may  be  thus  defined.      White,  we  may  say,  is 
the  colour  we  observe  in  snow  or  milk,    heat  the  sen- 
sation produced  by  approaching  the  fire,  and  so  in  in- 
numerable other  instances.     But  tiiese,  and  all  others 


OF  LOGIC.  35 

of  the  like  kind,  are  by  no  means  definitions,  exciting 
new  ideas  in  the  understanding,  but  merely  contri- 
vances to  remind  us  of  known  ideas,  and  teach  their 
connexion  with  the  established  names.  It  is,  neverthe- 
less, worth  our  notice,  that  what  logicians  call  defi- 
nitions of  the  name,  extend  properly  no  farther  than 
these  explanations,  serving  to  mark  the  connexion  of 
our  ideas  and  words  ;  and  are  therefore  justly  account- 
ed arbitrary,  inasmuch  as  the  connexions  themselves 
are  altogether  so. 

Sec.  XIX.... .Complex  ideas  alone  capable  of  that  kind 
of  description  which  goes  by  the  name  of  a  defnition* 

But  now  in  definitions  properly  so  called,  we  first 
consider  the  term  we  use,  as  the  sign  of  some  inward 
conception,  either  annexed  to  it  by  custom,  or  our  own 
free  choice  ;  and  then  the  business  of  the  definition  is 
to  unfold  and  explicate  that  idea.  As  therefore  the 
whole  art  lies,  in  giving  just  and  true  copies  of  our 
ideas  ;  a  definition  is  then  said  to  be  perfect,  when  it 
serves  distinctly  to  excite  the  idea  described  in  the 
mind  of  another,  even  supposing  him  before  wholly  un* 
acquainted  with  it.  This  point  settled,  let  us  next  en- 
quire into  what  those  ideas  are  which  are  capable  of 
being  thus  unfolded.  And  in  the  first  place,  it  is 
evident,  that  all  our  simple  ideas  are  necessarily  ex- 
cluded. We  have  seen  already,  that  experience  ahxne 
is  to  be  consulted  here,  insomuch,  that  if  either  the 
objects,  whence  they  are  derived,  come  not  in  our  way, 
or  the  avenues  appointed  by  nature  for  their  reception 
are  wanting,  no  description  is  sufficient  to  convey  them 
into  the  mind.  But  where  the  understanding  is  alrea- 
dy supplied  with  these  original  and  primitive  concep- 
tions, as  they  maybe  united  together  in  an  inficity  of 
different  forms  ;  so  may  all  their  several  combinations 
be  distinctly  laid  open  by  enumerating  the  simple  ideas 
concerned  in  the  various  collections,  and  tracing  the 
order  and  manner  in  which  they  are  linked  one  to  ano- 
ther. Now  these  combinations  of  simple  notices  con- 
stitute what  we  call  our  complex  notions  ;  whence  it  is 
evident  that  complex  ideas,  and  those  alone,  admit  of 

H 


86  DUNCAN'S  ELEMENTS 

that  kind  of  description,  which  goes  by  the  name  of  a 
definition. 

Sec  XX,  When  a  complex  idea  may  be  said  to  be  ful- 
ly unfolded* 
The  business  of  definitions  is  now,  I  think,  pretty- 
plain.  They  are,  as  we  have  seen,  pictures  or  repre- 
sentations of  our  ideas  ;  and  as  these  representations 
are  then  only  possible,  when  the  ideas  themselves  are 
complex  ;  it  is  obvious  to  remark,  that  definitions  can- 
not have  place,  but  where  we  make  use  of  terms, 
standing  for  such  complex  ideas.  But  perhaps  the  rea- 
der may  still  expect,  that  we  should  enter  a  little  more 
particularly  into  the  nature  of  a  definition,  describe  its 
parts,  and  show  by  what  rules  it  ought  to  proceed,  in 
order  to  the  attainment  of  its  proper  end.  To  give, 
therefore,  what  satisfaction  we  are  able  upon  this  point, 
Yre  must  again  call  to  mind,  that  the  design  of  a  defini- 
tion is,  se  to  unfold  the  idea  answering  to  any  term,  as 
that  it  may  be  clearly  and  distinctly  transferred  into 
the  mind  of  another.  But  now  our  complex  ideas, 
■which  alone  arc  capable  of  this  kind  of  description, 
being,  as  we  have  said,  nothing  more  than  diiferent 
combinations  of  simple  ideas  ;  we  then  know  and  com- 
prehend them  perfectly,  when  we  know  the  several 
simple  ideas  of  which  they  consist,  and  can  so  put  thern 
together  in  our  minds,  as  is  necessary  towards  the 
framing  of  that  peculiar  connexion,  which  gives  every 
idea  its  distinct  and  proper  appearance. 

Sec.  XXI.... Two  things  required  in  a  definition  :  tt 
enumerate  the  ideas,  and  explain  the  manner  of  their 
combination. 

Two  things  are  therefore  required  in  every  defini- 
tion. First,  that  all  the  original  ideas,  out  of  which 
the  complex  one  is  formed,  be  distinctly  enumerated. 
Secondly,  that  the  order  and  manner  of  combining 
them  into  one  conception,  be  clearly  explained.  Where 
a  definition  has  these  requisites,  nothing  is  wanting  to 
its  perfection  ;  because  every  one  who  reads  it,  and  un- 
derstands the  terms,  seeing  at  once  what  idea*  he  is 
t»  j6in  together,  and  also  in  what  manner,  can  at  plea- 


OF  LOGIC.        ,  M 

sure  form  in  his  own  mind  the  complex  conception 
answering  to  the  term  defined.  Let  us,  for  instance, 
suppose  the  word)  square,  to  stand  for  that  idea,  by 
which  we  represent  to  ourselves  a  figure,  whose  sides 
subtend  quadrants  of  a  circumscribed  circle;  The  parts 
of  this  idea,  are  the  sides  bounding  the  figure.  These 
must  be  four  in  nftmber,  and  all  equal  among  them- 
selves, because  they  are  each  to  subtend  a  fourth  part 
of  the  same  circle.  But  besides  these  component 
parts,  we  must  also  take  notice  of  the  manner  of  put- 
ting them  together,  if  we  would  exhibit  the  precis© 
idea,  for  which  the  word  square  here  stands.  For  four 
equal  right  lines,  any  how  joined,  will  not  subtend 
quadrants  of  a  circumscribed  circle.  A  figure  with 
this  property,  must  have  its  sides  standing  also  at 
right  angles.  Taking  in,  therefore,  this  last  conside- 
ration, respecting  the  manner  of  combining  the  parts, 
the  idea  is  fully  described,  and  the  definition  thereby 
rendered  complete*  For  a  figure,  bounded  by  four 
equal  sides,  joined  together  at  right  angles,  has  the 
property  required  ;  and  is,  moreover,  the  only  right* 
lined  figure  to  which  that  property  belongs* 

Sec.  XXII.... How  nve  are  to  proceed,  to  arrive  at  just 
and  adequate  definitions . 

And  now,  I  imagine,  it  will  be  obvious  to  every 
one  in  what  manner  we  ought  to  proceed,  in  order  to 
arrive  at  just  and  adequate  definitions.  First,  we  are 
to  take  an  exact  view  of  the  idea  to  be  described,  trace 
it  to  its  original  principles,  and  mark  the  several  sim- 
ple preceptions  that  enter  into  the  composition  of  it. 
.  Secondly,  we  are  to  consider  the  particular  manner  in 
which  these  elementary  ideas  are  combined,  in  order  to 
the  forming  of  that  precise  conception,  for  which  the 
term  we  make  use  of  stands.  When  this  is  done,  and 
the  idea  wholly  unravelled,  we  have  nothing  more  to 
do,  than  fairly  transcribe  the  appearance  it  makes  to 
our  own  minds.  Such  a  description,  by  distinctly  ex- 
hibiting the  order  and  number  of  our  primitive  con- 
ceptions, cannot  fail  to  excite,  at  the  same  time,  in  the 
mind  of  every  one  that  reads  it,  the  complex  idea  r«- 


83  DUNCAN'S  ELEMENTS 

suiting  from  them  ;  and  therefore  attains  the  true  and 
proper  end  of  a  definition. 


e&ap.  vii. 

OF  THE  COMPOSITION  AND  RESOLUTION 

OF  OUR  IDEAS,  AND  THE  RULES  OF 

DEFINITION  THENCE  ARISING. 

Sec.   L. ..In  compounding  our  Ideas,  we  proceed  by  sue* 

»  cessive  gradation. 

THE  rule,  laid  down  in  the  foregoing  chapter  is, 
general,  extending  to  all  possible  cases  ;  and  js, 
indeed,  that  to  which  alone  we  can  have  recourse, 
■where  any  doubt  or  difficulty  arises.  It  is  not,  how- 
ever, necessary,  that  we  should  practise  it  in  every  par- 
ticular instance.  Many  of  our  ideas  are  extremely 
complicated  ;  insomuch  that  to  enumerate  all  the  sim- 
ple preceptions  out  of  which  they  are  formed,  would  be 
a  very  troublesome  and  tedious  work.  For  this  rea- 
son, logicians  have  established  certain  compendious 
rules  of  defining,  of  which  it  may  not  be  amiss  here  to 
give  some  account.  But  in  order  to  the  better  under- 
standing of  what  follows,  it  will  be  necessary  to  ob- 
serve, that  there  is  a  certain  gradation  in  the  com- 
position of  our  ideas.  The  mind  of  man  is  very  li- 
mited in  its  views,  and  cannot  take  in  a  great  number 
.  of  objects  at  once.  We  are,  therefore,  fain  to  proceed 
by  steps,  and  make  our  first  advances  subservient  to 
those  which  follow.  Thus  in  forming  our  complex 
notions,  we  begin  at  first  with  but  a  few  simple  ideas,  • 
such  as  we  can  manage  with  ease,  and  unite  them  to- 
gether into  one  conception.  When  we  are  provided 
•with  a  sufficient  stock  of  these,  and  have,  by  habit 
and  use,  rendered  them  familiar  to  our  minds,  they  be- 
come the  component  parts  of  other  ideas,  still  more 
complicated,  and  form  what  we  may  call  a  second  or- 
der of  compound  notions.  This  process,  as  is  evident^ 
may  be   continued  to  any  degree  ©f  composition  wt 


OF  LOGIC.  89 

please,   mounting  from  one  stage  to  another,  and  en- 
larging the  number  of  combinations. 
Sec.   11... .Hence  ideas  of  this  class  best  comprehended) 

when  vje  advance  gradually  through  all  the  several 

orders. 

But  now  in  a  series  of  this  kind,  whoever  would 
acquaint  himself  perfectly  with  the  last  and  hightst 
order  of  ideas,  finds  it  much  the  most  expeditious  me- 
thod,  to  proceed  gradually  through  all  the  intermedi- 
ate steps.  For  was  he  to  take  a»y  very  compounded 
idea  to  pieces,  and  without  regard  to  t]*e  several 
classes  of  simple  perceptions,  that  have  already  been 
formed  into  distinct  combinations,  break  in  at  once 
into  its  original  principles,  the  number  would  be  so 
great,  as  perfectly  to  confound  the  imagination,  and 
^overcome  the  utmost  reach  and  capacity  of  the  mind. 
When  we  see  a  prodigious  multitude  of  men,  jumbled 
together  in  crowds,  without  order,  or  any  regular  po- 
sition, we  find  it  impossible  to  arrive  at  an  exact  know- 
ledge of  their  number.  But  if  they  are  formed  into 
separate  battalions,  and  so  stationed  as  to  fall  within 
the  leisurely  survey  of  the  eye  ;by  viewing  them  succes- 
sively, and  in  order  we  come  to  an  easy  and  certain  de- 
termination. It  is  the  same  in  our  complex  ideas. 
"When  the  original  preemptions,  out  of  which  they  are 
framed,  are  very  numerous,  it  is  not  enough  that  we 
take  a  view  of  them  in  loose  and  scattered  bodies.  We 
must  form  them  into  distinct  classes,  and  unite  these 
classes  in  a  just  and  orderly  manner,'  before  we  can  ar- 
rive at  a  true  knowledge  of  the  compound  notices  re- 
sulting from  them. 

Sec.  111.,, .Our  Definitions  ought  to  keep  pace  with  our 
Ideas,  atfd  observe  alike  gradation. 

This  gradual  progress  of  the  mind  to  its  compound 
notions,  through  a  variety  of  intermediate  steps,  plain- 
ly points  out  the  manner  of  conducting  the  definitions 
by  which  these  notions  are  conveyed  into  the  minds  of 
others.  For  as  the  series  begins  with  simple  >and  easjr 
combinations,  and  advances  through  a  succession  of 
different  orders,  rising  one  above  another  in  the  de- 
gree of  composition  j  it  is  evident,  that  in  a  train  of  de« 
H  2 


$0  DUNCAN'S  ELEMENTS 

tnitiohs  expressing  these  ideas,  a  like  gradation  is  to 
be  observed.  Thus  the  complex  ideas  of  the  lowest  or- 
der, can  no  otherwise  be  described,  than  by  enumerat- 
ing the  simple  ideas  out  of  which  they  are  made,  and 
explaining  the  manner  of  their  union.  But  then  in 
the  second,  or  any  succeeding  order,  as  they  are  form- 
ed out*  of  those  gradual  combinations,  that,  constitute 
the  inferior  classes,  it  is  not  necessary  in  describing 
them,  to  mention  one  by  one,  all  the  simple  ideas  of 
which  they  consist.  They  may  be  more  distinctly  and 
briefly  unfolded,  by  enumerating  the  compound  ideas  of 
a  lower  order  from  whose  union  they  result,  and  which 
are  all  supposed  to  be  already  known,  in  consequence  of 
previous  definitions.  Here  then  it  is,  that  the  logical 
method  of  defining  takes  place  ;  which  that  we  may  the 
better  understand,  I  shall  explain  somewhat  more  par- 
ticularly, the  several  steps  and  gradations  of  the  mind, 
in  compounding  its  ideas,  and  thence  deduce  that  pecu- 
liar form  of  a  definition,  which  logicians  have  thought 
jit  to  establish. 

See.  IV....  The  steps  by  which  the  Mind  proceeds  from 
Particular  to  General  Ideas. 
All  the  ideas  we  receive,  from  the  several  objects  of 
mature  that  surround  us,  represent  distinct  individuals. 
These  individuals,  when  compared  together,  are  found 
in  certain  particulars  to  resemble.  Hence,  by  collect- 
ing the  resembling  particulars  into  one  conception,  we 
forra  the  notion  of  a  species.  And  here  let  it  be  ob- 
served, that  this  last  idea  is  less  complicated  than  that 
ky  which  we  represent  any  of  the  particular  objects 
contained  under  it.  For  the  idea  of  the  species  ex- 
cludes the  peculiarities  of  the  several  individuals,  and 
retains  only  such  properties  as  are  common  to  them  all. 
Again,  by  comparing  several  species  together,  and  ob- 
serving their  resemblance,  we  form  the  idea  of  the 
genus  ;  where,  in  the  same  manner  as  before,  the  com- 
position is  lessened,  because  we  leave  out  what  is  pecu- 
liar to  the  several  species  compared,  and  retain  only  the 
particulars  wherein  they  agree.  It  is  easy  to  conceive 
the  mind,  proceeding  thus  from  one  step  to  another, 
aud  advancing  through  its  several  classes  of  general  no- 


OF  LOGIC.  »1 

S 

tions,  until  at  last  it  comes  to  the  highest  genus  of 
all,  denoted  by  the  word  beings  where  the  bare  idea  of 
existence  is  only  concerned. 

Sec.  V....T/j<?  conduct  of  the  Mind  in  compounding  its 
Ideas,  as  it  advances  through  the  different  orders  of 
preception. 

In  this  procedure,  we  see  the  mind  unravelling  a 
complex  idea,  and  tracing  it  in  the  ascending  scale,  from 
greater  to  less  degrees  of  composition,  until  it  termi- 
nates in  one  simple  preception.  If  now  we  take  the 
series  the  contrary  way,  and  beginning  with  the  last 
or  highest  genus,  carry  our  view  downwards,  through 
all  the  inferior  genera  and  species,  quite  to  the  indivi- 
duals ;  we  shall  thereby  arrive  at  a  distinct  apprehen- 
sion of  the  conduct  of  the  understanding  in  compound- 
ing its  ideas.  For  in  the  several  classes  of  our  pre- 
ceptions,'the  highest  in  the  scale  is,  for  the  most  part, 
made  up  ©f  but  a  few  simple  ideas,  suck  as  the  mind 
can  take  in  and  survey  with  ease.  This  first  general 
notion,  when  branched  out  into  the  different  subdivi- 
sions contained  under  it,  has  in  every  one  of  them 
something  peculiar,  by  which  they  are  distinguished 
among  themselves ;  insomuch  that  in  descending  from 
the  genus  to  the  species,  we  always  superadd  some 
new  idea,  and  thereby  increase  the  degree  of  composi- 
tion. Thus  the  idea  denoted  by  the  word  figure,  is 
of  a  very  general  nature,  and  composed  of  but  few  sim- 
ple preceptions,  as  implying  no  more  than  space  every 
where  bounded.  But  if  we  descend  farther,  and  con- 
sider the  boundaries  of  this  space,  as,  that  they  may 
be  either  lines  or  surfaces,  we  fall  into  the  several  spe« 
cies  of  figure.  For  where  the  space  is  bounded  by  one 
or  more  surfaces,  we  give  it  in  the  name  of  a  solid fgure  $ 
but  where  the  boundaries  are  lines,  it  is  called  a  plain 
figure. 

Sec.  VI...  .The  Idea  of  the  Species  formed  by  superadd 

ding  the  specific  Difference  to  the  Genus* 

In  this  view  of  things,  it  .is  evident,   that  the  spe* 

cies  formed  by  superadding  a  new  idea  to  the  genus* 

Here,  for  instance,  the  genus  is  circumscribed  space. 


92  DUNCAN'S  ELEMENTS 

If  now  to  this  we  superadd  the  idea  of  a  circumscrip- 
tion by  line,  we  frame  the  notion  of  that  species  of 
figures  which  are  called  plain  ;  but  if  we  conceive  the 
circumscription  to  be  by  surfaces,  we  have  the  spe- 
cies of  solid  figures*  This  superadded  idea  is  called 
the  specific  difference,  not  only  as  it  serves  to  divide 
the  species  from  the  genus,  but  because,  being  differ- 
ent in  all  the  several  subdivisions,  we  thereby  also  dis- 
tinguish the  species  one  from  another.  And  as  it  is 
likewise  that  conception,  which*,  by  being  joined  to 
the  general  idea,  completes  the  notion  of  the  species  ; 
hence  it  is  plain,  that  the  genus  and  specific  difference 
are  to  be  considered  as  the  proper  and  constituent  parts 
of  the  species*  If  we  trace  the  progress  of  the  mind 
still  farther,  and  observe  it  advancing  through  the  in- 
ferior species,  we  shall  find  its  manner  of  proceeding 
to  be  always  the  same.  For  every  lower  species  is 
formed  by  superadding  some  new  idea  to  the  species 
next  above  it.  ;  insomuch,  that  in  descending  the  scale 
©four  preceptions,*.the  understanding  passes  through 
different  orders  of  complex  notions,  which  become  more 
and  more  complicated  at  every  step  it  takes.  Let  us 
resume  here,  for  instance,  the  species  of  plain  figures. 
They  imply  no  more  than  space  bounded  by  lines. 
But  if  we  take  in  an  additional  consideration  of  the 
nature  of  these  lines,  as,  whether  they  are  right  or 
curves,  we  fall  into  the  subdivisions  of  plain  figure, 
distinguished  by  the  ■names  rectilinear,  curvilinear  and 
mixtilinear* 

Sec.  VII,.,, And  in  all  the  inferior  species  by  superad- 
ding the  specific  to  the  nearest  genus. 
And  here  we  arc  to  observe,  that  though  plain 
figures,  when  considered  as  one  of  those  branches  that 
come  under  the  notion  of  figure  in  general,  take  the 
name  of  a  species  ;  yet  compareU  with  the  classes  of 
curvilinear,  rectilinear,  aid  mixtilinear,  into  which 
they  themselves  may  be  divided,  they  really  become  a 
genus,  of  which  the  before-n.entiqned  subdivisions  con- 
stitute the  several  species.  These  species,  in  the  same 
manner  as  in  the  case  of  plain  and  solid  figures,  con- 
sist of  the  genus  and  specific  difference,  as  their  con*. 


• 

OF  LOGIC.  9* 

stituent  parts.  For  in  the  curvilinear  kind,  the  cur* 
vity  of  the  lines  bounding  the  figure,  makes  what  is 
called  the  specific  difference  ;  to  which  if  we  join  the 
genus,  which  here  is  plain  figure;  or  space  circumscrib- 
ed by  lines,  we  have  all  that  is  necessary  towards  com- 
pleting the  notion  of  the  species.  We  are  only  to 
take  notice,  that  this  last  subdivision,  having  two  ge- 
nera above  it,  viz.  plain  figure,  and  figure  in  general; 
the  genus,  joined  with  the  specific  difference,  in  order 
to  constitute  the  species  of  curvilinear,  is  that  which 
lies  nearest  to  the  said  species.  It  is  the  notion  of 
plain  figure,  and  not  of  figure  in  general,  that,  joined 
with  the  idea  of  curvity,  makes  up  the  complex  -con- 
ception of  curve-lined  figures.  For  in  this  descending 
scale  of  our  ideas — Figure  in  general,  plain  figures, 
curve-lined  figures — the  two  first  are  considered  as  ge- 
nera in  respect  to  the  third ;  and  the  second  in  order, 
or  that  which  stands  next  to  the  third,  is  called  the 
nearest  genus.  But  now  as  it  is  this  second  idea, 
which,  joined  with  the  notion  of  curvity,  forms  the  spe- 
cies of  curve-lined  figures ;  it  is  plain,  that  the  third  or 
last  idea  in  the  series,  is  made  up  of  the  nearest  genus 
and  specific  difference.  This  rule  holds  invariably, 
however  far  the  series  is  continued  ;  because  in  a  train 
of  ideas  thus  succeeding  one  another,  all  that  precede 
the  last  are  considered  as  so  many  genera,  in  respect  of 
that  last;  and  the  last  itself  is  always  formed,  by  su- 
peradding the  specific  difference  to  the  genus  next  it. 

Sec.  V  III....  T/ie  idea  of  an  individual  composed  of  tbt 
lowest  species  and  numeric  difference. 

Here  then  we  have  an  universal  description,  applica- 
ble to  all  our  ideas,  of  whatever  kind,  from  the  high- 
est genus,  to  the  lowest  species.  For  taking  them  in 
order  downwards  from  the  said  general  idea,  they  eve- 
ry where  consist  of  the  genus  proxi mum,  and  differen- 
tia specifica,  as  logicians  love  to  express  themselves. 
But  when  we  come  to  the  lowest  species  of  all,  com- 
prehending it  only  individuals,  the  superadded  idea, 
by  which  these  individuals  are  distinguished  one  front 
another,  no  longer  takes  the  name  of  the  specific  differ* 


94  DUNCAN'S  ELEMENTS 

ence.  For  here  it  serves  not  to  denote  distinct  spe- 
cies, but  merely  a  variety  of  individuals,  each  of  which* 
having  a  particular  existence  of  its  own,  is  therefore 
numerically  different  from  every  other  of  the  same 
kind.  And  hence  it  is,  that  in  this  last  case,  logici- 
ans choose  to  call  the  superadded  idea  by  the  name  ©f 
the  numerical  difference  ;  insomuch  that  as  the  idea  of 
a  species,  is  made  up  of  the  nearest  genus  and  specific 
difference,  so  the  idea  of  an  individual  consists  of  the 
lowest  species  and  numeric  difference.  Thus  the  circle 
is  a  species  of  curve-lined  figures,  and  what  we  call  the 
lowest  species,  as  comprehending  under  it  only  indivi- 
duals. Circles  in  particular  are  distinguished  from  one 
another  by  the  length  and  position  of  their  diameters. 
The  length,  therefore,  and  position  of  the  diameter  of 
a  circle,  is  what  logicians  call  the  numerical  differ- 
ence;  because  these  being  given,  the  circle  itself  may 
be  described,  and  an  individual  thereby  constituted. 

Sec.  IX.....  Definitions  to  follow  one  another  in  train, 
and  pass  through  the  same  successive  gradations  as 
cur  compound  ideas. 

And  thus  we  have  endeavoured  to  trace,  in  theiest 
manner  we  are  able,  the  progress  of  the  mind  jn  com* 
.  pounding  its  ideas.  It  begins,  we  see,  with  the  most 
general  notions,  which  consisting  of  but  a  few  simple 
notices,  are  easily  combined  and  brought  together  into 
one  conception.  Thence  it  proceeds  to  the  species  com- 
prehended under Hhis  general  idea,  and  these  are  form- 
ed by  joining  together  the  genus  and  specific  difference. 
And  as  it  often  happens,  that,  these  species  may  be  still 
further  subdivided,  and  run  on  in  along  series  of  con- 
tinued gradations,  producing  various  orders  of  com- 
pound perceptions  ;  so  ail  these  several  orders  are  regu- 
larly and  successively  formed,by  annexing  in  every  step, 
the  specific  difference  to  the  nearest  genus.  When  by  this 
method  of  procedure,  we  are  come  to  the  lowest  order 
of  all  ;  by  joining  the  species  and  numeric  difference,  we 
frame  the  ideas  of  individuals.  And  here  the  series  ne- 
cessarily terminates,  because  it  is  impossible  any  farther 
to  bound  or  limit  our  conceptions.     This  view  of  tht 


OF  LOGIC.  98 

composition  of  our  ideas,  representing  their  constituent 
parts  in  every  step  of  the  progression,  naturally  points 
out  the  true  and  genuine  form  of  a  definition.  For  as 
definitions  are  no  more  than  descriptions  of  the  ideas  for 
Which  the  terms  defined  stand;  and  as  ideas  are  then 
described,  when  we  enumerate  distinctly  and  in  order, 
the  parts  of  which  they  consist  ;  it  is  plain,  that  by 
making  our  definitions  follow  one  another,  according 
to  the  natural  train  of  our  conceptions,  they  will  be  sub- 
ject to  the  same  rules,  and  keep  pace  with  the  ideas 
they  describe. 

Scc«  X....  The  form  of  a  Definition  in  all  the  various 
orders  of  Conception. 
As  therefore  the  first  order  of  our  compound  notions, 
er  the  ideas  that  constitute  the  highest  genera,  in  the 
different  scales  of  perception,  are  formed,  by  uniting 
together  a  certain  number  of  simple  notices  ;  so  the 
terms  expressing  these  genera,  are  defined  by  enumera- 
ting the  simple  notices,  so  combined.  And  as  the  species 
comprehended  under  any  genus,  or  the  complex  ideas 
e>f  the  second  order,  arise  from  superadding  the  specific 
difference  to  the  said  general  idea;  so  the  definition  of 
the  names  of  the  species  is  absolved,  in  a  detail  of  the 
ideas  of  the  specific  difference,  connected  with  the  term  of 
the  genus.  For  the  genus  having  been  before  defined,  the 
term  by  which  it  is  expressed  stands  for  a  known  idea, 
and  may  therefore  be  introduced  into  all  subsequent  de*. 
finitions,  in  the  same  manner  as  the  names  of  simple 
perceptions.  It  will  now,  I  think,  be  sufficiently  obvious, 
that  the  definitions  of  all  the.  succeeding  orders  of  com- 
pound notions,  will  every  where  consist  oj  the  term  of 
the  nearest  genus  joined  with  an  enumeration  of  the  ideas 
that  constitute  the  specific  difference ;  and  that  the  defini- 
tion of  individuals  unites  tiu  name  of  the  lowest  species) 
with  the  terms  by  which  we  express  the  ideas  of  the  nu- 
meric difference.  . 

Sec.  XL...  The  logical  method  of  defining  perfect  in  its 
kind  ; 
IJere  then  we  have  the  true   and  proper  form  of  a 
ie£uition#  ia   all    tke   various  orders   of  ccmceptioa* 


36  DUNCAN'S  ELEMENTS 

This  is  that  method  of  defining,  which  is  commonly 
called  logical,  and  which,  we  see,  is  perfect  in  its  kind, 
inasmuch  as  it  presents  a  full  and  adequate  description 
of  the  idea,  for  which  the  term  defined  stands.  There 
are  still  two  things  worthy  of  observation,  before  wc 
take  leave  of  this  subject.  First,  that  the  very  frame 
and  contexture  of  these  definitions,  points  out  the  order 
in  which  they  ought  to  follow  one  another.  For  as 
the  name  of  the  genus  is  admitted  into  a  description, 
only  in  consequence  of  its  having  been  before  defined  ; 
it  is  evident,  that  we  must  pass  gradually  through  all 
the  different  orders  of  conception.  Accordingly,  logi- 
cians lay  it  down  as  a  rule,  that  we  are  to  begin  always 
with  the  highest  genus,  and  carry  on  the  series  of  de- 
finitions regularly,  through  all  the  intermediate  genera 
and  species,  quite  down  to  the  individuals.  By  this 
means  our  descriptions  keep  pace  with  our  ideas,  and 
pass  through  the  same  successive  gradations  ;  insomuch, 
that  the  perusal  of  them  must  excite  those  ideas  in  the 
understanding  of  another,  in  the  very  order  and  man- 
ner in  which  they  are  put  together  by  the  mind  in  its 
uniform  advances  from  simple  to  the  most  complicated 
notions.  Now  this  is  the  true  and  proper  end  of  de- 
fining, and  indeed  the  highest  perfection  of  that  art. 

Sec.  XII.  And  applicable  to  all  words  whatsoever  ca- 
pable of  a  definition* 

There  is  yet  another  thing  to  be  observed  on  this 
head,  namely,  that  the  form  here  prescribed,  is  appli- 
cable to  all  words  whatsoever,  capable  of  a  defini- 
tion. For  as  every  term  we  use,  must  denote  some  idea, 
either  general  or  particular  ;  and  as  all  our  complex 
notions  relating  to  both  these  classes  of  perception  from 
the  highest  genus  quite  down  to  the  individuals,  come 
within  the  rules  of  description  here  given  ;  it  is  evi- 
dent, that  this  particular  manner  of  unfolding  an  idea, 
may  be  extended  to  all  the  possible  complex  concep- 
tions we  can  connect  with  our  words.  By  the  rules 
therefore  of  this  method,  definitions  may  be  applied  to 
all  terms  standing  for  complex  ideas  ;  and  as  these,  by 
what  we  have  shown,  at  large  in  the  two  foregoing 


OF  LOGIC.  9f 

chapters,  are  the  only  definable  articles  of  speech  ;  it 
necessarily  follows,  that  the  directions  here  given  arc 
universal,  extend  to  all  particular  instances,  and  arc 
alike  applicable  in  all  languages.  And  thus  at  length) 
we  have  not  only  deduced  that  peculiar  form  of  a  defi- 
nition which  obtains  among  logicians,  but  shown  it 
also  to  be  perfect  in  its  kind,  and  to  take  in  the  whole 
compass  of  language. 


BOOK.  II. 

OF  JUDGMENT,  OR  INTUITION. 


Cfmp*  I. 

OF  THE  GROUNDS  OF  HUMAN 
JUDGMENT. 

Sec.  I..... Intuition  respects  the   relations  between  out 
Ideas  when  they  are  immediately  perceivable, 

WHEN  the  mind  is  furnished  with  ideas,  its  next 
step  in  the  way  to  knowledge  is,  the  compa- 
ring these  ideas  together,  in  order  to  judge  of  their 
agreement  or  disagreement.  In  this  joint  view  of  our 
idea;,  if  the  relation  is  such,  as  to  be  immediately  dis- 
coverable by  the  bare  inspection  of  the  mind  ;  the  judg- 
ments thence  obtained  are  called  intuitive,  from  a  word 
that  denotes  to  look  at :  for  in  this  case,  a  mere  atten- 
tion to  the  ideas  compared,  suffices  to  let  us  see,  how 
far  they  are  connected  or  disjoined.  Thus,  that  the 
whole  is  greater  than  any  of  its  parts,  is  an  intuitive 
judgment,  nothing  more  being  required,  to  convince 
us  of  its  truth,  than  an  attention  to  the  ideas  of  whole 
and  part.  And  this,  too,  is  the  reason,  why  we  call 
I 


$8  DUNCAN'S  ELEMENTS 

the  act  of  the  mind  forming  these  judgments  intuition  3 
as  it  is  indeed  no  more  than  an  immediate  perception 
of  the  agreement  or  disagreement  of  any  two  ideas. 

Sec.  II... .Experience  and  Testimony  the  Ground  of 
judging  as  to  Facts* 
But  here  it  is  to  be  observed,  that  our  knowledge  of 
this  kind,  respects  only  our  Ideas,  and  the  relations 
between  them,  and  therefore  can  serve  only  as  a  foun- 
dation to  such  reasonings,  as  are  employed  in  investi- 
gating these  relations.  Now  it  so  happens,  that  many 
of  our  judgments  are  conversant  about  facts,  and  the 
real  existence  of  things  which  cannot  be  traced  by  the 
bare  contemplation  of'our  ideas.  It  does  not  follow, 
because  I  have  the  idea  of  a  circle  in  my  mind,  that 
therefore  a  figure  answering  to  that  idea,  has  a  real  , 
existence  in  nature.  I  can  form  to  myself  the  notion 
of  a  centaur,  or  golden-  mountain,  but  never  imagine 
on  that  account,  that  either  of  them  exists.  What 
then  are  the  grounds  of  our  judgments,  in  relation  to 
facts  ?  I  answer,  these  two  :  experience  and  testimony* 
By  experience  we  are  informed  of  the  existence  of  the 
several  objects  which  surround  us,  and  operate  upon 
our  senses.  Testimony  is  of  a  wider  extent,  and  reaches 
not  only  to  objects  beyond  the  present  sphere  of  our 
.observation,  but  also  to  facts  and  transactions,  which, 
being  now  past,  and  having  no  longer  any  existence, 
could  not,  without  this  conveyance,  have  fallen  under 
ourcognizance. 

Sec.  III....  Three  Foundations  of  human  Judgement* 
viz.  1.  Intuition*  the  Ground  of  scientifcal  know- 
ledge ; 

Here  then  we  have  three  foundations  of  human 
judgment,  from  which  the  whole  system  of  our  know- 
ledge may  with  ease  and  advantage  be  deduced.  First, 
intuition*  which  respects  our  ideas  themselves,  and 
their  relations,  and  is  the  foundation  of  that  species  of 
reasoning,  which  we  call  demonstration*  For  whate- 
ver is  deduced  from  our  intuitive  perceptions,  by  a 
clear  and  connected  aeries  of  proofs,  is  said  to  be  de- 
monstrated, and  produces   absolute  certainty   in  the 


OF  LOGIC.  99 

mind.  Hence  the  knowledge  obtained  in  this  manner, 
is  what  we  properly  term  science  ;  because,  in  every 
step  of  the  procedure,  it  carries  its  own  evidence  along 
with  it,  and  leaves  no  room  for  doubt  or  hesitation* 
And  what  is  highly  worthy  of  notice  ;  as  the  truths 
of  this  class  express  the  relations  between  our  ideas, 
and  the  same  relations  must  ever  and  invariably  sub- 
sist between  the  same  ideas,  our  deductions,  in  the  way 
of  science,  constitute  what  we  call  eternal,  necessary, 
and  immutable  truths.  If  it  be  true,  that  the  whole 
is  equal  to  all  its  parts,  it  must  be  so  unchangeably  j 
because  the  relations  of  equality  being  attached  to  the 
ideas  themselves,  must  ever  intervene  where  the  same 
ideas  are  compared.  Of  this  nature  are  all  the  truths 
of  natural  religion,  morality,  and  mathematics  ;  and  in 
general  whatever  may  be  gathered  from  the  bare  view 
and  consideration  of  our  ideas. 

Sec.  IV.. ..2.  Experience  the  Ground  of  our  Knowledge 
of  the  Powers  and  Qualities  of  Bodies. 

The  second  ground  of  human  judgment  is  experience  ; 
from  which  we  infer  the  existence  of  those  objects  that 
surround  us,  and  fall  under  the  immediate  notice  of  our 
senses.  When  we  see  the  sun,  or  cast  our  eyes  towards 
a  building,  we  not  only  have  ideas  of  these  objects 
within  ourselves,  but  ascribe  to  them  a  real  existence 
out  of  the  mind.  It  is  also  by  the  information  of  the 
senses,  that  we  judge  of  the  qualities  of  bodies  ;  as 
when  we  say  that  snow  is  white,  fire  hot,  or,  steel 
hard.  For  as*  we  are  wholly  unacquainted  with  the  in- 
ternal structure  and  constitution  of  the  bodies  that 
produce  these  sensations  in  us,  nay,  and  are  unable  to 
trace  any  connexion  between  that  structure  and  the 
sensations  themselves,  it  is  evident  that  we  build  our 
judgments  altogether  upon  observation,  ascribing  to 
bodies  such  qualities  as  are  answerable  to  the  percep- 
tions they  excite  in  us.  But  this  is  not  the  only  ad- 
vantage derived  from  experience,  for  to  that,  too,  are 
we  indebted  for  all  our  knowledge  regarding  the  co- 
existence of  sensible  qualities  in  objects,  and  the  ope- 
rations of   bodies  one  upon  another.     Ivory,  for  in- 


100  DUNCAN'S  ELEMENTS 

stance,. is  hard  and  elastic  ;   this   we  know  by  experi- 
ence, and  indeed  by  that  alone.    For  being  altogether 
strangers  to  the  true  nature  both  of  elasticity  and  hard- 
ness,   we    cannot,    by   the  bare  contemplation  of  our 
ideas,  determine  how  far  the   one    necessarily   implies 
the   other,  or  whether  there  may  not  be  a  repugnance 
between  them.      But  when  we  observe  them  to  exist 
botli^  in  the  same  object,    we  are    then   assured    from 
experience  that  they  are  not  incompatible  ;   and  when 
■we  also  find,  that  a  stone  is  hard  and  not  elastic — and 
that  air,  though  elastic,  is  not  hard — we  also  conclude, 
upon  the  same  foundation,   that  the  ideas  are  not    ne- 
cessarily conjoined,  but  may  exist  separately  in   differ- 
ent objects.   In  like  manner,  with  regard  to  the  opera- 
tions of  bodies,  one  upon  another,  it  is  evident,   that 
our  knowledge  this  way    is  all  derived  from    observa- 
tion.    Aqua  regia  dissolves  gold,  as  has  been  found  by 
frequent  trial  ;    nor  is  there  any  other  way  of  arriving 
at  the  discovery.  Naturalists  may  tell  us,  if  they  please, 
that  the  parts  of  aqua  regia  are  of  a  texture  apt  to  in- 
sinuate between   the  corpuscles-  of  gold,    and    thereby 
loosen  and  shake  them  asunder.       If  this  is  a  true  ac- 
count of  the  matter,  I  believe  it  will,  notwithstanding, 
be  allowed,  that  our  conjecture,  in  regard  to  the  con- 
formation of  these  bodies,  is  deduced  from  the  experi- 
ment, and  not  the  experiment  from  the  conjecture.    It 
was  not  from  any  previous  knowledge  of  the  intimate 
structure  of  aqua  regia    and  gold)  and  the  aptness  of 
their  parts  to  act  or  be  acted  upon,     that  we  came  by 
the  conclusion  above  mentioned.     The  internal  consti- 
tution of  bodies  is  in  a  manner  wholly  unknown  to  us: 
and  could  we  even  surmount  this  difficulty,  yet  as  the 
separation  of  the  parts  of  gold  implies  something  like 
an  active  force  in  the  menstruum,    and  we  are  unable 
to  conceive  how  it  comes  to  be  possessed  of  this  acti- 
vity ;  the  effect  must  be  owned  to  be  altogether  beyond 
our  comprehension.   But  when  repeated  trials  had  once 
continued  it,  insomuch  that  it  was  admitted  as  an  esta- 
blished truth  in  natural  knowledge,  it   was  then  easy 
for  men  to  spin  out  theories  of  their   own  invention, 
and  contrive  such  a    structure   of  parts  both  for  gold 


OR  LOGIC.  101 

*nd  aqua  regia,  as  would  best  seYve  to4  explain  the 
phenomenon,  upon  the  principles  of  that-  .system  of 
philosophy  they  had-  adopted.  '  .1  n^ighc  easily' show, 
from  innumerable  other  instances,  how  much  our 
knowledge  of  the  mutual  action  of  bodies  depends  upon 
observation-  The  bite  of  a  viper  will  kill.  Plants  are 
some  salutary,  others  noxious.  Fire  dissolves  one  body, 
and  hardens  another.  These  are  truths  generally 
known  ;  nor  is  it  less  evident  that  we  owe  their  disco- 
very wholly  to  experience. 

Sec.  \  ....Why  many  yseful  Inventions  owe  their  Birth 
to  Chance. 
And  hence  it  is  easy  to  account  for  what  to  some 
writers  has  appeared  a  very  great  paradox  ;  that  many 
of  the  most  important  inventions  in  human  life  have 
taken  their  rise  from  chance,  and  instead  of  coming* 
out  of  the  schools  of  philosophers,  are  for  the  most 
part  ascribed  to  men  of  no  figure  in  the  commonwealth 
of  learning.  Sowing,  planting,  the  use  of  compass, 
and  such  like,  are  not  deductions  of  human  reason, 
but  discoveries  which  owe  their  birth  to  observation 
and  trial.  No  wonder,  therefore,  if  these  inventions 
derived  their  beginning  from  such,  as,  being  engaged 
in  the  active  and  busy  scenes  of  life,  were"  more  in  the 
way  of  those  experiments  which  lead  to  discoveries  of 
this  nature.  And  here,  as  the  particular  callings  and 
professions  of  men,  and  oft-times  chance,  has  a  great 
ascendant,  it  need  not  seem  strange,  if  some  of  the 
most  useful  arts  in  society  appear  to  have  had  an  ori- 
ginal purely  casual. 

Sec.  VI.. ..Natural    Knowledge,  from  the   Grounds  on 
which  it  rests,  aptly  termed  experimental  Philosophy. 
From  what  has  been  said,  it  is  evident,  that  as  intu- 
ition   is    the  foundation  of  what    we    cull  scientifical.} 
knowledge,  so  is  experience  of  natural.    For   this  last 
being  wholly  taken   up  with  the  objects  of  sense,  or 
those   bodies  that  constitute  the   natural  world — and 
their  properties,  as  far  as  wTe  can  discover  them,   being 
to  be  traced  only  by  a  long  and  painful  series  of  obser« 
vations  j   it  is  apparentj  that  in  order  to  improve  this. 
I  2 


102  DUNCAN'S  ELEMENTS 

branch  of  knowledge,  fve 'must  betake  ourselves  to  the 
Jiiet-iod  $>£  ti:ial  afnd /xperimtent.  Accordingly,  we  find, 
that  v;!ike  thi's  was  neglected,'  ihtle  advance  was  made 
In  the  philosophy  of  nature  ;  whereas  a  contrary  pro- 
ceeding has  enriched  the  present  age  with  many  valu- 
able discoveries  ;  insomuch  that  natural  knowledge,  in 
allusion  to  the  foundation  on  which  it  stands,  has  been 
very  aptly  called  experimental  philosophy. 

Sec.  VII. ...Though  much  of  our  Knowledge  of  Body 
depends  on  Testimony,  yet  Experience  is  the  ulti- 
mate Foundation  of  it. 

But  though  experience  is  what  we  may  term  the  im- 
Miediate  foundation  of  natural  knowledge,  yet  with  re- 
spect to  particular  persons,  its  influence  is  very  nar- 
row and  confined.  The  bodies  that  surround  us  are 
numerous  ;  many  of  them  lie  at  a  great  distance  ;  and 
some  quite  beyond  our  reach.  Life  too  is  short,  and 
so  crowded  with  cares,  that  but  little  time  is  left  for 
any  single  man  to  employ  himself  in  unfolding  the 
mysteries  of  nature.  Hence  it  is  necessary  to  admit 
many  things  upon  the  testimony  of  others,  which,  by 
this  means,  becomes  the  foundation  of  a  great  part  of 
cur  knowledge  of  body.  No  man  doubts  of  the  power 
of  aqua  regia  to  dissolve  gold,  though  perhaps  he  ne- 
ver himself  made  the  experiment.  In  these,  therefore, 
and  such  like  cases,  we  judge  of  the  facts,  and  opera- 
tions of  nature,  upon  the  mere  ground  of  testimony. 
However,  as  we  can  always  have  recourse  to  experi- 
ence, where  any  doubt  or  scruple  arises,  this  is  justly 
considered  as  the  true  foundation  of  natural  philoso- 
phy being  indeed  the  ultimate  support  upon  which  our 
assent  rests,  and  whereto  we  appeal,  when  the  highest 
degree  of  evidence  is  required. 

Sec.  VIII.  3.  Testimony  the  Ground  of  Historical 
Knowledge. 
But  there  are  many  facts  that  will  not  allow  of  an 
appeal  to  the  senses,  and  in  this  case  testimony  is  the 
true  and  only  foundation  of  our  judgments.  All  hu- 
man actions,  of  whatever  kind,  when  considered  as 
already  past,  are  of  the  nature  here  described  j  because 


OF  LOGIC.  105 

having  now  no  longer  any  existence,  both  the  facts 
themselves,  and  the  circumstances  attending  them, 
can  be  known  only  from  the  relations  of  such  as  had 
sufficient  opportunities  of  arriving  at  the  truth.  Testi- 
mony, therefore,  is  justly  accounted  a  third  ground  of 
human  judgment:  and  as  from  the  other  two  we  have 
deduced  scientijical  and  natural  knowledge,  so  may  we 
from  this  derive  historical ;  by  which  I  would  be  un- 
derstood to  mean,  not  merely  a  knowledge  of  the  civil 
transactions  of  states  and  kingdoms,  but  of  all  facts 
whatsoever,  where  testimony  is  the^ultimate  founda- 
tion of  our  belief. 

Sec.  IX....  The  second  Operation  of  the  Mind,  common* 
ly  extended  beyond  Intuition* 
Before  I  conclude  this  chapter,  it  will  be  necessary 
to  observe,  that  though  the  second  operation  of  the 
mind,  properly  speaking,  extends  not  beyond  intuitive 
perceptions,  yet  logicians  have  not  confined  themselves 
to  so  strict  a  view  of  it ;  but  calling  ft  by  the  name 
judgment,  thereby  denote  all  acts  of  the  mind,  where 
only  two  ideas  are  compared,  without  the  immediate 
interposition  of  a  third.  For  when  the  mind  joins  or 
separates  two  ideas,  though  perhaps  this  is  done  in 
coBsequence  of  a  train  of  previous  reasoning,  yet  if  the 
understanding  proceeds  upofTestablished  notions,  with- 
out attending  to  that  train  of  reasoning,  its  determi- 
nations are  still  considered  as  acts  of  judgment.  Thus, 
That  God  created  the  universe,  that  men  are  accounta- 
ble/or their  actions,  are  frequently  mentioned  by  logici- 
ans, as  instances  of  the  mind  judging.  And  yet  it  is 
apparent,  that  these  judgments  are  by  no  means  of  the 
kind  we  call  intuitive  ;  nay,  that  it  requires  mucli  ex- 
ercise of  the  reasoning  faculty,  before  a  man  can  trace 
their  connexion  with  the  perceptions  of  that  name.  I 
could  in  the  same  manner  easily  show,  that  even  our 
judgments  of  experience  and  testimony,  when  pursued 
to  their  source,  derive  all  their  power  of  persuasion, 
from  being  linked  with  intuitive  truths.  But  I  shall 
wave  this  enquiry  for  the  present,  as  being  of  a  nature 
too  subtile  for  a  work  of  this  kind.  The  remark  itself, 
however,  was  needful,  as  well  to  illustrate  the  proper 


104  DUNCAN'S  ELEMENTS 

distinction  between  the  powers  of  the  understanding* 
as  to  explain  the  reason,  why  hi  this  part  of  logic,  we 
extend  the  second  operation  of  the  mind  beyond  those 
limits,  that  in  strictness  of  speech  belong  to  it.  Let  us 
now  proceed  to  consider  a  little  more  particularly  the 
nature  and  variety  of  these  our  judgments. 


Cfmp-  ii. 


OF  AFFIRMATIVE  AND  NEGATIVE 
PROPOSITIONS. 

Sec.  I.....77i£  subject  and  predicate  vf  a  Proposition 
explained. 

WHILE  the^comparing  of  our  ideas  is  considered 
merely  as  an  act  of  the  mind,  assembling  them 
together,  and  joining  or  disjoining  them  according  to 
the  result  of  its  perceptions,  we  call  it  judgment ;  but 
when  our  judgments  are  put  into  words,  they  then  bear 
the  name  of  propositions.  A  proposition,  therefore,  is  a 
sentence  expressing  some  judgment  of  the  mind,  where- 
by two  or  more  ideas  are  affirmed  to  agree  or  disagree. 
Now,  as  our  judgments  include  at  least  two  ideas,  one 
of  which  is  affirmed  or  denied  of  the  other,  so  must  a 
proposition  have  terms  answering  to  these  ideas.  The 
idea,  of  which  we  affirm  or  deny,  and  of  course  the 
term  expressing  that  idea,  is  called  the  subject  of  the 
proposition.  The  idea  affirmed  or  denied,  as  also  the 
term  answering  it,  is  called  the  predicate.  Thus  in  the 
proposition,  God  is  omnipotent :  G&d  is  the  subject,  it 
being  of  him  that  we  affirm  omnipotence  ;-  and  omni- 
potence is  the  predicate,  because  we  affirm  the  idea,  ex- 
pressed by  that  word  to  belong  to  God. 

Sec.  II The  Copula,  &c* 

But  as  in  propositions,  ideas  are  either  joined  or 
disjoined  ;  it  is  not  enough  to  have  terms  expressing 
those  ideas,  unless  we  have  also  some  words  to  denote 


OF  LOGIC.  105 

their  agreement  or  disagreement.  That  word  in  a  propo- 
sition, which  connects  two  ideas  together,  is  called  the 
copula;  and  if  a  negative  particle  be  annexed,  we 
thereby  understand,  that  the  ideas  are  disjoined.  The 
substantive  verb  is  commonly  made  use  of  for  the  co- 
pula, as  in  the  above-mentioned  proposition,  God  is 
omnipotent  ;  where  it  represents  the  copula,  and  signi- 
fies  the  agreement  of  the  ideas  God  and  omnipotence* 
But  if  we  mean  to  separate  two  ideas,  then,  besides  the 
substantive  verb,  we  must  also  use  some  particle  of  ne- 
gation, to  express  this  repugnance.  The  proposition, 
man  is  not  perfect,  may  serve  as  an  example  of  this 
kind,  where  the  notion  of  perfection,  being  removed 
from  the  idea  of  man,  the  negative  particle,  not,  is  in- 
serted after  the  copula,  to  signify  the  disagreement  be- 
tween the  subject  and  predicate. 

Sec.  III.. ..Propositions  sometimes  expressed  by  a  single 
word. 
Every  proposition  necessarily  consists  of  these  three 
parts;  but  then  it  is  not  alike  needful,  that  they  be  all 
severally  expressed  in  words  ;  because  the  copula  is  of- 
ten included  in  the  term  of  the  predicate  ;  as  when  we 
say,  he  sits;  which  imports  the  same  as  he  is  sitting. 
In  the  Latin  language,  a  single  word  has  often  the  force 
of  a  whole  sentence.  Thus  ambujat  is  the  same,  as  Hie 
est  ambulans ;  amo,  as  ego  sum  amans  ;  and  so  in  innu- 
merable  other  instances  ;  by  which  it  appears,  that  we 
are  not  so  much  to  regard  the  number  of  words  in  a 
sentence,  as  the  ideas  they  represent,  and  the  manner 
in  which  they  are  put  together.  For  whenever  two 
ideas  are  joined  or  Disjoined  in  an  expression,  though 
of  but  a  single  word,  it  is  evident,  that  we  have  a  sub- 
ject, predicate,  and  copula,  and  of  consequence  a  com- 
plete proposition. 

Sec.  IV.. ..Affirmative  and  Negative  Propositions. 

When  the  mind  joins  two  ideas,  we  call  it  an  affirma- 
tive judgment  ;  when  it  separates  them,  a  negative  ; 
and  as  any  two  ideas  compared  together,  must  necessa- 
rily either  agree  or  not  agree,  it  is  evident,  that  all  our 
judgments   fell  under  these   two   divisions.    Hence, 


t06    .      DUNCAN'S  ELEMENTS 

likewise,  the  proposition  expressing  these  judgments, 
are  all  either  affirmative  or  negative.  An  affirmative 
proposition  connects  the  predicate  with  the  subject,  as, 
a  stone  is  heavy  :  a  negative  proposition  separates  them, 
as  God  is  not  the  author  of  evlk  Affirmation,  there- 
fore, is  the  same  as  joining  two  ideas  together;  and 
this  is  done  by  means  of  the  copula.  Negation,  on  the 
contrary,  marks  a  repugnance  between  the  ideas  com- 
pared ;  in  which  case  a  negative  particle  must  be  called 
in,  to  show  that  the  connexion*  included  in  the  copula. 
does  not  take  place. 

Sec.  V ....When  the  negative  particle  serves  to  disjoin 
ideas. 

And  hence  we  see  the  reason  of  the  rule  commonly 
laid  down  by  logicians,  that  in  all  negative  proposi- 
tions, the  negation  ought  to  affect  the  copula.  For  as 
the  copula,  when  placed  by  itself,  between  the  subject 
and  the  predicate,  manifestly  binds  them  together  ;  it 
is  evident,  that  in  order  to  render  a  proposition  nega- 
tive, the  particle  of  negation  must  enter  it  in  such  man- 
ner, as  to  destroy  this  union.  In  a  word,  then  only  are 
two  ideas  disjoined  in  a  proposition,  when  the  negative 
particle  may  be  so  referrccLto  the  copula,  as  to  break  the 
affirmation  included  in  it,  and  undo  that  conpexion  it 
would  otherwise  establish.  When  we  say,  for  instance, 
no  man  is  perfect ;  take  away  the  negation,  and  the  co- 
pula of  itself  plainly  unites  the  ideas  in  the  proposition. 
But  as  this  is  the  very  reverse  of  what  is  intended,  a 
negative  mark  is  added,  to  fchow  that  this  union  does 
not  here  take  place.  The  negation,  therefore,  by  de- 
stroying the  effect  of  the  copula,  changes  the  very  na- 
ture of  the  proposition,  insomuch  that  instead  of  bind- 
ing two  ideas  together,  it  denotes  their  separation.  On 
the"contrary,  in  this  sentence,  the  man  who  departs  not 
from  an  upright  behavipur,  is  beloved  of  God  ;  the  pre- 
dicate, beloved  of  Gud>  is  evidently  affirmed  of  the  sub- 
ject an  upright  man-;  so  that  notwithstanding  the  nega- 
tive particle,  the  proposition  is  still  affirmative.  The 
reason  is  plain  ;  the  nagation  here  affects  not  the  copu- 
la,  but  making  properly,  a  part  of  the  subject,  serves, 


OF  LOGIC.  107 

with  other  terms  in  the  sentence,  to  form  one  complex 
idea,  of  which  the  predicate,  beloved  of  God,  is  directly 
affirmed.  This,  perhaps,  to  some  may  appear  a  mere 
logical  refinement,  contrived  to  justify  the  scholastic 
rule  for  distinguishing  between  affirmative  and  nega- 
tive propositions.  But  if  it  be  considered,  that  this  dis- 
tinction is  of  great  importance  in  reasoning,  and  can- 
not in  many  cases  be  made  with  certainty,  but  by  means 
of  this  criterion  here  given,  the  reader  will  see  suffici- 
ent reason  for  my  taking  so  much  pains  to  illustrate  it. 

Sec.  VI.., .How  a  Copula  comes  to  be  a  part  of  a  ne- 
gative proposition. 

Perhaps  it  may  still  appear  a  mystery,  how  a  copu- 
la can  be  said  to  be  a  part  of  a  negative  proposition, 
whose  proper  business  it  is  to  disjoin  ideas.  This  dif- 
ficulty, however,  will  vanish,  if  we  call  to  mind,  that 
every  judgment  implies  a  direct  affirmation,  and  that 
this  affirmation  alone  makes  the  true  copula  in  a  propo- 
sition. But  as  our  affirmations  are  of  two  kinds,  viz.  ei- 
ther of  agreement  or  of  disagreement,  between  the  ideas 
compared;  hence  there  is  also  a  twofold  expression  of 
our  judgments.  In  the  case  of  agreement,  the  copula 
alone  suffices;  because  it  is  the  proper  mark  whereby 
we  denote  an  identity  or  conjunction  of  ideas.  But 
where  perceptions  disagree,  there  we  must  call  in  a  ne- 
gative particle  :  and  this  gives  us  to  understand  that 
the  affirmatipn  implied  in  the  copula,  is  not  of  any. con- 
nexion between  the  subject  and  predicate,  but  of  their 
mutual  opposition  and  repugnance. 

Cfrap.  in. 

OF  UNIVERSAL  AND  PARTICULAR 
PROPOSITIONS. 

Sec.   I,.. .Division   of  Propositions,  into  Universal  and     Jt-. 

Particular. 

f  T^HE  next  considerable  division  of  propositions,  is 

A    into  universal  and  particular.  Our  ideas,  accord- 


103         DUNCAN'S  ELEMENTS 

ing  to  what  has  been  already  observed  in  the  first  part," 
are  all  singular,  as  they  enter  the  mind,  and  repre- 
sent individual  objects.  But  as  by  abstraction  we  can 
render  them  universal,  so  as  to  comprehend  a  whole 
class  of  things,  and  sometimes  several  classes  at  once  ; 
hence  the  terms  expressing  these  ideas  must  be  in 
like  manner  universal.  If,  therefore,  we  suppose  any 
general  term  to  become  the  subject  of  a  proposition* 
it  is  evident,  that  whatever  is  affirmed  of  the  abstract 
idea  belonging  to  that  term  may  be  affirmed  of  all 
the  individuals  to  which  that  idea  extends.  Thus  when 
we  say,  men  jare  mortal ;  we  consider  mortality,  not  as 
confined  to  one  or  any  number  of  particular  men, 
but  as  what  may  be  ♦affirmed  without  restriction  of 
the  whole  species.  By  this  means,  the  proposition  be* 
comes  as  general  as  the  idea  which  makes  the  subject 
of  it,  and  indeed  derives  its  universality  entirely  from 
that  idea,  being  more  or  less  so,  according  as  this  may 
be  extended  to  more  or  fewer  individuals.  But  it  is 
further  to  be  observed  of  these  general  terms,  that  they 
sometimes  enter  a  proposition  in  their  full  latitude, 
as  in  the  example  given  above ;  and  sometimes  appear 
with  a  mark  of  limitation.  In  this  last  case,  we  are 
given  to  understand,  that  the  predicate  agrees  not  to 
the  whole  universal  idea,  but  only  to  a  part  of  it  ; 
as  in  the  proposition,  some  men  are  wise  :  for  here 
wisdom  is  not  affirmed  of  every  particular  man,  but 
restrained  to  a  few  of  the  human  species. 

SectII„;Propositio?is  universal  where  the  subject  is  so} 
without  a  mark  of  restriction* 

Now  from  this  different  appearance  of  the  general 
idea,  that  constitutes  the  subject  of  any  judgment,  ari- 
ses the  division  of  propositions  into  universal  and/;ar- 
ticular.  An  universal  proposition  is  that,  wherein  the 
subject  is  some  general  term,  taken  in  its  full  latitude, 
insomuch  that  the  predicate  agrees  to  all  the  individuals 
comprehended  under  it,  if  it  denotes  a  proper  species  ; 
and  to  all  the  several  species  and  their  individuals,  if 
it  marks  an  idea  of  a  higher  order.  The  words,  a//, 
eve rj>}  no}  none9  Ike.  are  the  proper  signs  of  this  univer* 


OF  LOGIC.  109 

satity  ;  and  as  they  seldom  fail  to  accompany  general 
truths,  so  they  are  the  most  obvious  criterion  whereby 
to  distinguish  them*  All  animals  have  a  power  of  be* 
ginning  motion*  This  is  an  universal  proposition  ;  as 
we  know  from  the  word  all,  prefixed  to  the  subject 
animal,  which  denotes  that  it  must  be  taken  in  its 
full  extent.  Hence  the  power  of  beginning  motion 
may  be  affirmed  of  all  the  several  species  of  aaimals  ; 
as  of  birds,  quadrupeds,  insects,  fishes,  Sec.  and  of  all 
the  individuals  of  which  these  different  classes  consist, 
as  of  this  hawk,  that  horse,  and  so  for  others. 

Sec.  III,*:Propositions  particular  where  seme  utiiQer* 
sal  Subjects  appear  with  a  Mark  of  Limitation* 

A  particular  proposition  has  in  like  manner  some  ge- 
neral term  for  its  subject,  but  with  a  mark  of  limita- 
tion added,  to  denote,  that  the  predicate  agrees  only  to 
some  of  the  individuals  comprehended  under  a  species, 
or  to  one  or  more  of  the  species  belonging  to  any  ge- 
nus, and  not  to  the  whole  universal  idea.  Thus,  some 
stones  are  heavier  than  iron  ;  some  men  have  an  uncom- 
mon share  of  prudence.  In  the  last  of  these  proposi- 
tions, the  subject,  some  men,  implies  only  a  certain 
number  of  individuals,  comprehended  under  a  single 
species.  In  the  former,  where  the  subject  is  a  genus, 
that  extends  to  a  great  variety  of  distinct  classes, 
some  stones  may  not  only  imply  any  number  of  particu- 
lar stones,  but  also  several  whole  species  of  stones  ; 
inasmuch  as  there  may  be  not  a  tew,  with  the  property- 
there  described.  Hence  we  see,  that  a^proposition  does 
not  cease  to  be  particular,  by  the  predicate's  agreeing 
to  a  whole  species,  unless  that  species,  singly  and  dis- 
tinctly considered,  makes  also  the  subject  of  which  we 
affirm  or  deny.  For  if  it  belongs  to  some  genus,  that 
has  other  specie?  under  it,  to  which  the  predicate  does 
not  agree  ;  it  is  plain,  that  where  this  genus  is  that  of 
which  we  affirm  or  deny,  the  predicate  agreeing  only 
to  a  part  of  it,  and  not  to  the  whole  general  idea,  con* 
stitutes  the  proposition  particular. 
K 


iio  DUNCAN'S  ELEMENTS 

Sec.  TV."..*.  A  sure  and  infallible  Criterion,  whereby  t» 
distinguish  between  universal  and  particular  Proposi- 
tions, 

Here  then,  we  have  a  sure  and  infallible  mark, 
■whereby  to  distinguish  between  universal  and  particu- 
lar propositions.  Where  the  predicate  agrees  to  all  the 
individuals  comprehended  under  the  notion  of  the  sub- 
ject, there  the  proposition  is  universal  ;  where  it  be- 
longs only  to  some  of  them,  or  to  some  of  the  species 
of  the  general  idea,  there  the  proposition  is  particular. 
This  criterion  is  of  easy  application,  and  much  safer 
than  to  iepend  upon  the  common  signs  of  all,  every , 
some,  none,  &c.  because  these  being  different  in  dif- 
ferent languages,  and  often  varying  in  their  significa- 
tion, are  very  apt  in  many  cases  to  mislead  the  judg- 
ment. Thus  if  we  say,  all  the  soldiers  -when  drawn 
Tip,  formed  a  square  of  a  hundred  men  a  side  :  it  is  evi- 
dent that  the  predicate  cannot  be  affirmed  of  the  sever- 
al individuals,  but  of  the  whole  collective  idea  of  the 
subject ;  whence,  by  the  rule  given  above,  the  proposi- 
tion is  not  "universal.  It  is  true,  logicians  lay  down 
many  observations,  to  enable  us  to  distinguish  aright 
on  this  head  :  but  if  the  criterion  here  given  be  duly 
attended  to,  it  will  be  of  more  real  service  to  us  than 
an  hundred  rules.  For  it  is  infallible,  and  may  be  ap. 
plied  with  ease;  whereas  the  directions,  which  we  meet 
with  in  treatises  of  logic,  being  drawn  for  the  most  part, 
from  the  analogy  of  language,  and  common  forms  of 
speech,  are  not  only  burdensome  to  the  memory,  but  of- 
ten very  doubtful  and  uncertainin  their  application. 

Sec.   V Singular  Propositions  contained  under    the 

head  of  particulars. 

There  is  still  one  species  of  propositions  that  remains 
te  be  described  ;  and  which  the  more  deserves  our  no- 
tice, as  it  is  not  yet  agreed  among  logicians,  to  which 
of  the  two  classes  mentioned  above,  they  ought  to  be 
referred.  I  mean  singular  propositions  \  or  those  wiiere 
the  subject  is  an  individual.  Of  this  nature  are  the  fol- 
lowing :  sir  Isaac  Newton  was  the  inventor  of  fusions  ; 
this  book  contains  mqny  useful  truths*     What  occasions 


OF  LOGIC.  Ill 

some  difficulty,  as  to  the  proper  rank  of  these  proposi- 
tions, is,  that  the  subject  being  taken  according  to  the 
whole  of  its  extension,  they  sometimes  have  the  same 
effect  in  reasoning,  as  universals.  But  if  it  be  con- 
sidered, that  they  are,  in  truths  the  most  limited  kind 
of  particular  propositions,  and  that  no  proposition  can, 
with  any  propriety,  be  called  universal,  but  where  the 
subject  is  some  universalidea  ;  we  shall  not  be  long  in 
determining  to  which  class  they  ought  to  be  referred. 
When  we  say,  some  books  contain  useful  truths,  the 
proposition  is  particular  ;  because  the  general  term  ap- 
pears with  a  mark  of  restriction.  If,  therefore,  wre  say, 
this  book  contains  useful  truths  ;  it  is  evident,  that  the 
proposition  must  be  still  more  particular,  as  the  limita- 
tion, implied  in  the  word,  this,  is  of  a  more  confined 
nature,  than  in  the  former  case,  I  know,  there  are  in- 
stances, where  singular  propositions  have  the  same  ef- 
fect in  reasoning,  as  universals  ;  yet  is  not  this,  by  rea- 
son of  any  proper  universality,  belonging  to  them  ;  but 
because  the  conclusion,  in  such  cases  being  always  sin- 
gular, maybe  proved  by  a  middle  term  which  is  also 
singular  ;  as  I  could  easily  demonstrate,. were  this  a  pro- 
per place  for  entering  into  a  discussion  of  that  nature* 

Sec.  YL.. .The  Fourfold  Division  of  Propositions* 

:  We  see,  therefore,  that  all  propositions  are  either 
affirmative  or  negative  ;  nor  is  it  less  evident,  that  in 
both  cases,  they  be  universal  or  particular.  Hence 
arises  that  celebrated  fourfold  division  of  them,  into 
universal  affirmative,  and  universal  negative  ;  parties 
lar  affirmative,  and  particular  negative ;  which  com- 
prehends, indeed  all  their  varieties.  The  use  of  this 
method  of  distinguishing  them  will  appear  more  fully 
afterwards,  when  we  come  to  treat  of  reasoning  and 
syllogism.  , 


112  DUNCAN'S  ELEMENTS 


e&ap.  IV. 

OF  ABSOLUTE  AND  CONDITIONAL 
PROPOSITIONS. 

*ec.   J.:*Bistinction  of  Qualities  into  Essential  and 
Accidental. 

THE  objects,  about  which  we  are  chiefly  convers- 
ant in  this  world,  are  all  of  a  nature  liable  to 
change.  What  may  be  affirmed  of  them  at  one  time 
cannot  often  at  another  ;  and  it  makes  no  small  part 
cf  our  knowledge  to  distinguish  rightly  these  varia- 
tions, and  trace  the  reasons  upon  which  they  depend. 
Tor  it  is  observable,  that  amidst  all  the  vicissitudes  of 
nature,  some  things  remain  constant  and  invariable  ; 
nor  are  even  the  changes  to  which  we  see  others  liable, 
effected,  but  in  consequence  of  uniform  and  steady 
laws,  which,  when  known,  are  sufficient  to  direct  us  in 
cur  judgments  about  them.  Hence  philosophers,  in 
distinguishing  the  objects  of  our  perception  into  vari- 
ous classes,  have  been  very  careful  to  note,  that  some 
properties  belong  essentially  to  the  general  idea,  so  ai 
not  to  be  separable  from  it  but  by  destroying  its  very- 
nature  ;  while  others  are  only  accidental,  and  may  be 
affirmed  or  denied  of  it,  in  different  circumstances. 
Thus,  solidity,  a  yellow  colour,  and  great  weight,  arc 
considered  as  essential  qualities  of  gold  ;  but  whether 
it  shall  exist  as  an  uniform,  conjoined  mass,  is  not 
alike  necessary.  We  see  that  by  a  proper  menstruum, 
it  may  be  reduced  to  a  fine  powder  ;  and  that  intense 
heat  will  bring  it  into  a  state  of  fusion. 

jSec.  !!»*••* Hence  a  considerable  Diversity  in  our  Man- 
ner of  judging* 
Now,  from  this  diversity  in  the  several  qualities  of 
things,  arises  a  considerable  difference  as  to  the  man- 
ner of  our  judging  about  them.  For  in  this  first  place, 
all  such  properties,  as  are  inseparable  from  objects, 
when  considered  as  belonging  to  any  genus  or  species, 
are  affirmed  absolutely  and  without  reserve,  of  that  ge- 


OF  LOGIC.  113 

tieral  idea.  Thus  we  say  ;  gold  is  very  weighty  ;  a 
stone  is  hard ;  animals  have  a  power  of  self-motion. 
But  in  the  case  of  mutable  or  accidental  qualities,  as 
they  depend  upon  some  other  consideration,  distinct 
from -the  generalidea  ;  that  also  must  be  taken  into  the 
account,  in  order  to  form  an  accurate  judgment.  Should 
we  afRrm,  for  instance,  of  some  stones,  that  they  are 
very  susceptible  of  a  rolling  motion  ;  the  proposition, 
while  it  remains  in  this  general  form,  cannot  with  any* 
advantage  be  introduced  into  our  reasonings.  An  apt- 
ness to  receive  that  mode  of  motion  flows  from  the  fi- 
gure of  the  stone  ;  which,  as  it  may  vary  infinitely,  our 
judgment  then  only  becomes  applicable  aud  determin- 
ate, when  the  particular  figure,  of  which  volubility  is  a 
consequence,  is  also  taken  into  the  account.  Let  us 
then  bring  in  this  other  consideration,  and  the  proposi- 
tion will  run  as  follows  :  stones  of  a  spherical  form  are 
easily  put  into  a  rolling  motion*  Here  we  see  the  con- 
dition upon  which  the  predicate  is  affirmed,  and  there- 
fore know  in  what  particular  cases  the  proposition  may- 
be applied. 

Sec.   III.. ..Which  gives  rise  to  the  division  of  Proposi- 
tions into  Absolute  and  Conditional. 

This  consideration  of  propositions,  respecting  the 
manner  in  which  the  predicate  is  affirmed  of  the  subject, 
gives  rise  to  the  division  of  them  into  absolutt  and  con- 
dtTional.  Absolute  propositions  are  those,  wherein  we 
affirm  some  property  inseparable  from  the  idea  of  the 
subject,  and  which,  therefore,  belongs  to  it  in  all  possi- 
ble cases  ;  as,  God  is  infinitely  wise  :  virtue  tends  to  the 
ultimate  happiness  of  man.  But  where  the  predicate  is 
not  necessarily  connected  jadth  the  idea  of  the  subject, 
unless  upon  some  consideration  distinct  from  that  idea, 
there  the  proposition  is  called  conditional.  The  reason 
of  the  name  is  taken  from  the  supposition  annexed, 
which  is  of  the  nature  cf  a  condition,  and  may  be  ex* 
pressed  as  such.  Thus  ;  if  a  stone  is  exposed  to  the  rays 
of  the  s uny  it  will  contract  some  degree  of  heat.  If  a 
river  runs  in  a  very  declining  channel^  its  rapidity  wilt 
€oustantly  increase. 

K  2 


114  DUNCAN'S  ELEMENTS 

Sec.  TV*,,, The  great  importance  of  this  division)  as  it 
renders  Propositions  determinate  ; 

There  is  not  any.  thing  of  greater  importance  in  phi- 
losophy, than  a  due  attention  to  this  division  of  pro- 
positions. If  we  are  careful  never  to  affirm  things  abso- 
lutely, but  where  the  ideas  are  inseparably  conjoined  ; 
and  if,  in  our  other  judgments,  we  distinctly  mark  the 
conditions,  which  determine  the  predicate  to  belong  to 
the  subject :  we  shall  be  the  less  liable  to  mistake,  in 
applying  general  truths  to  the  particular  concerns  of 
human  life.  It  is  owing  to  the  exact  observance  of 
this  rule,  that  mathematicians  have  been  so  "happy  in 
their  discoveries  ;  and  that  what  they  demonstrate  of 
magnitude  in  general,  may  be  applied  with  ease  in  all 
obvious  occurrences. 

Sec.  \T,,„And  reduces  them  from  particulars  to  ge- 
nerals. 

The  truth  of  it  is,  particular  propositions  are  then 
known  to  be  true,  when  we  can  trace  their  connexion 
•with  universals  :  and  it  is,  accordingly,  the  great  busi- 
ness of  science,  to  find  out  general  truths,  that  may  be 
applied  with  safety  in  all  obvious  instances.  Now  the 
great  advantage  arising  from  determining  with  care 
the  conditions  upon  which  one  idea  may  be  affirmed  or 
denied  of  another,  is  this  ;  that  thereby  particular  pro- 
positions really  become  universal,  may  be  introduced 
with  certainty  into  our  reasonings,  and  serve  as  stand- 
ards to  conduct  and  regulate  our  judgments.  To  illus- 
trate this  by  a  familiar  instance  :  if  we  say,  some  wa- 
ter acts  very  forcibly  ;  the  proposition  is  particular  : 
and  as  the  conditions,  on  which  this  forcible  action 
depends,  arc  not  mentioned,  it  is  as  yet  uncertain  in 
what  cases  it  may  be  applied.  Let  us  then  supply  these 
conditions,  and  the  proposition  will  run  thus  ;  water 
conveyed  in  sufficient  quantity  along  a  steep  descent, 
nets  very  forcibly.  Here  we  have  an  universal  judg- 
ment, inasmuch  as  the  predicate,  forcible  action,  may 
be  ascribed  to  all  water  under  the  circumstances  men- 
tioned. Nor  is  it  less  evident,  that  the  proposition  in 
this  new  form  is  of  easy  application  ;    and  in  fact  we 


OP  LOGIC.  lis 

find,  that  men  do  apply  it  in  instances  where  the  for- 
cible action  of  water  is  required  ;  as  in  corn-mills,  and 
many  other. works  of  art.  Thus  we  see,  in  what  man- 
ner we  are  to  proceed,  in  order  to  arrive  at  universal 
truths,  which  is  the  great  end  and  aim  of  science; 
And  indeed,  would  men  take  the  same  care,  duly  to 
express  the  conditions  on  which  they  affirm  and  deny, 
as  mathematicians  do,  in  those  theorems  which  they 
term  hypothetical,  I  doubt  not,  but  we  might  be  able 
to  deduce  many  truths,  in  other  parts  of  philosophy, 
with  no  less  clearness,  force,  and  perspicuity,  than  has 
hitherto  been  thought  peculiar  to  the  science  of  quantity. 


OF  SIMPLE  AND  COMPOUND 
PROPOSITIONS. 

Sec;    I,. ..Division    of  Propositions  into  Simple   and 
Compound, 

HITHERTO  we  have  treated  of  propositions, 
where  only  two  ideas  are  compared  together. 
These  are,  in  the  general,  called  simple  ;  because,  hav- 
ing but  one  subject  and  one  predicate,  they  are  the  ef- 
fect of  a  simple  judgment  that  admits  of  no  subdivi- 
sion. But  if  it  so  happens,  that  several  ideas  offer 
themselves  to  our  thoughts  at  once,  whereby  we  are 
led  to  affirm  the  same  thing  of  different  objects,  or  dif- 
ferent things  of  the  same  object ;  the  propositions,  ex- 
pressing these  judgments,  are  called  compound:  because 
they  may  be  resolved  into  as  many  others  as  there  are 
subjects  or  predicates  in  the  whole  complex  determina- 
tion of  the  mind.  Thus,  God  is  infinitely  wise  and  in* 
finitely  powerful;  here  there  are  two  predicates,  in* 
finite  wisdom  and  infinite  power,  both  affirmed  of  the 
same  subject  ;  and  accordingly,  the -proposition  may 
be  resolved  into  two  others,  affirming  these  predicates 
severally.  In  like  manner,  in  the  proposition,  neither 
kings  nor  people  are  exempt  from  death,  the  predicate 
is  denied  of  froth  subjects,  and  may  therefore  be  sepa* 


116  DUNCAN'S  ELEMENTS 

rated  from  them,  in  distinct  propositions.  Nor  is  it 
less  evident,  that  if  a  complex  judgment  consists  of 
several  subjects  and  predicates,  it  may  be  resolved  into 
as  many  simple  propositions  as  are  the  number  of  dif- 
ferent ideas  compared  together*  Riches  and  honours 
are  apt  to  elate  the  mind,  and  increase  the  number  of 
cur  desires.  In  this  judgment,  there  are  two  subjects 
and  twcvpredicates  :  and  it  is  at  the  same  time  apparent, 
that  it  may  be  resolved  into  four  distinct  propositions. 
Riches  are  apt  to  elate  the  mind.  Riches  are  apt  to 
increase  the  number  of  our  desires.  And  so  of  honours. 
Sec.  II.. ..The  proper  Notion  of  a  Compound  Proposi* 
tion  ascertained. 
Logicians  have  divided  these  compound  propositions 
into  a  great  many  different  classes  ;  but  in  my  opini- 
on; not  with  aNdiie  regard  to  their  proper  definition. 
Thus  conditionals,  casuals,  relatives,  itfe.  are  mention- 
ed as  so  many  distinct  species  of  this  kind,  though  in 
fact  they  are  ila  more  than  simple  propositions.  To 
give  an  instance  of  a  conditional  :  If  a  stone  is  expos- 
ed to  the  rays  of  the  sun,  it  will  contract  some  degree  of 
heat.  Here  we  have  but  one  subject  and  one  predi- 
cate ;  for  the  complex  expression,  A  stone  exposed  to 
the  rays  of  the  sun,  constitutes  the  proper  subject  of 
this  proposition,  and  is  no  more  than  one  determinate 
idea.  The  same  thing  happens  in  casuals.  Rehoboam 
•was  unhappy,  because  he  followed  evil  counsel.  P  aeny 
not,  that  there  is  here  an  appearance  of  two  proposi- 
tions arising  from  the  complexity  of  the  expression  ; 
but  when  we  come  to  consider  the  matter  more  near- 
ly, it  is  evident  that  we  have  but  a  single  subject  and 
predicate....  The  pursuit  of  evil  counsel  brought  misery 
upon  Rehoboam.  It  is  not  enough,  therefoie,  to  ren- 
der a  proposition  compound,  that  the  subject  and  pre- 
dicate are  complex  notions,  requiring  sometimes  a  whole 
sentence  to  express  them  ;  for  in  this  case,  the  com- 
parison is  still  confined  to  two  ideas,  and  constitutes 
what  we  call  a  simple  judgment.  But  where  there  are 
several  subjects  or  predicates,  or  both,  as  the  affirma- 
tion or  negation  may  be  alike  extended  to  then)  all,  the 
proposition,  expressing  such  a  judgment,  is  truly  a  coU 


OF  logic.  nr 

lection  of  as  many  simple  ones,  as  there  are  different 
ideas  compared.  Confining  onrselves,  therefore,  to 
this  more  strict  and  just  notion  of  compound  proposi- 
ons,  they  are  all  reducible  to  two  kinds,  viz.  copula- 
tives and  disjunctives. 

Sec.  III... .Compound  Propositions  either  Copulative. 

A  copulative  proposition  is,  where  the  subjects  and 
predicates  are  so  linked  together,  that  they  may  be  all 
severally  affirmed  or  den  ied  one  of  another.  Of  this  na- 
ture are  the  examples  of  compound  propositions  given 
above.  Riches  and  honours  are  apt  to  elate  the  mind,  and 
increase  the  number  of  our  desires.  Neither  kings  nor 
people  are  exempt  from  death.  In  the  first  of  these, 
the  two  predicates  may  be" affirmed  severally  of  each 
subject,  whence  we  have  four  distinct  propositions. 
The  other  furnishes  an  example  of  the  negative  kind, 
where  the- same  predicate  being  disjoined  from  both 
subjects,  may  be  also  denied  of  them  in  separate  pro* 
positions. 

Sec.  IV.... Or  Disjunctive. 
The  other  species  of  compound  propositions  are  those 
called  disjunctives  ;  in  which,  comparing  several  pre- 
dicates with  the  same  subject,  we  affirm,  that  one  of 
them  necessarily  belongs  to  it,  but  leave  the  particular 
predicate  undetermined.  If  any  one,  for  example, 
says  :  This  world  either  exists  of  itself  or  is  the  work 
of  some  all-wise  and  powerful  cause  ;  it  is  evident,  that 
one  of  the  two  predicates  must  belong  to  the  world  ; 
but  as  the  proposition  determines  not  which,  it  is 
therefore  of  the  kind  we  call  disjunctive.  Such,  too, 
are  the  following  :  The  sun  either  moves  round  the 
earth,  or  is  the  centre  about  which  the  earth  revolves. 
Friendship  finds  men  equal,  or  makes  them  so.  It  is  the 
nature  of  all  propositions  of  this  class,  supposing  the r» 
to  be  exact  in  point  of  form,  that  upon  determining  the 
particular  predicate,  the  rest  are  of  course  to  be  re- 
moved ;  or  if  all  the  predicates  but  one  are  removed  ; 
that  one  necessarily  takes  place.  Thus,  in  the  exam- 
ple above,  if  we  allow  the  world  to  be  the  work  of  some 
wise  and  powerful  cause,  we  of  course  deny  it  to  be 


118  DUNCAN'S  ELEMENTS 

self-existent  ;  or  if  we  deny  it  to  be  self-existent,  we 
must  necessarily  admit  that  it  was  produced  by  some  wise 
and  powerful  cause.  Now  this  particular  manner  of 
linking  the  predicates  together,  so  that  the  establishing 
one  displaces  all  the  rest. ...or  the  excluding  all  but  one 
necessarily  establishes  that  one... .cannot  otherwise  be 
effected  than  by  means  of  disjunctive  particles.  And 
hence  it  is",  that  propositions  of  this  class  take  their 
names  from  these  particles,  which  make  so  necessary  a 
part  of  them,  and  indeed,  constitute  their  very  nature, 
considered  as  a  distinct  species.  But  I  shall  reserve 
what  farther  might  be  said  on  this  head,  till  I  come  to 
treat  of  reasoning,  where  the  great  use  and  importance 
of  disjunctive  propositions  will  better  appear. 


Cfmp.  vi. 

OF  THE  DIVISION  OF  PROPOSITIONS  INTO  SELF- 
EVIDENT    AND  DEMONSTRABLE. 

Sec.  I Design  of  this  Chapter. 

AS  we  are  soon  to  enter  upon  the  third  part  of  lo- 
gic, which  treats  of  reasoning — and  as  the  art  of 
reasoning  lies  in  deducing  propositions  whose  truth 
does  not  immediately  appear,  from'  others  more  known 
-. — it  will  be  proper,  before  we  proceed  any  farther,  to 
examine  a  little  the  different  degrees  of  evidence  that 
accompany  our  judgments  ;  that  we  may  be  the  better 
able  to  distinguish  in  what  cases  we  ought  to  have  re- 
course to  reasoning,  and  what  those  propositions  are, 
upon  which,  as  a  sure  and  unerring  foundation,  we  may 
venture  to  build' the  truth  of  others. 

Sec.  II Propositions  divided  into   Self-evident   and 

Demonstrable, 
When  any  proposition  is  offered  to  the  view  of  the 
mind,  if  the  terms,  in  which  it  is  expressed,  are  under- 
stood ;  upon  comparing  the  ideas  together,  the  agree- 
ment or  disagreement  asserted  is  either  immediately  per- 
ceived, or  found  to  lie  beyond  the  present  reach  of  the 
understanding.  In  the  first  case,  the  proposition  is  said 


OF  LOGIC.  119 

to  be  self-evident^  and  admits  not  of  any  proof ;  because 
a  bare  attention  to  the  ideas  themselves  produces  full 
conviction  and  certainty ;  nor  is  it  possible  to  call  in 
any  thing,  more  evident  by  way  of  confirmation.  But 
where  the  connexion  or  repugnance  comes  not  so  readi- 
ly under  the  inspection  of  the  mind,  there  we  must  have 
recourse  to  reasoning  ;  a,nd  if  by  a  clear  series  of  proofs 
we  can  make  out  the  truth  proposed,  insomuch  that  self- 
evidence  shall  accompany  every  step  of  the  procedure, 
we  are  then  able  to  demonstrate  what  we  assert ;  and 
the  proposition  itself  is  said  to  be  demonstrable.  When 
we  affirm,  for  instance,  that  it  is  impossible  for  the  same 
thing  to  be  v and  not  to  be;  whoever  understands  the 
terms  made  use  of,  perceives  at  first  glance  the  truth  of 
what  is  asserted  ;  nor  can  he,  by  any  efforts,  bring  him- 
self to  believe  the  contrary.  The  proposition  therefore 
is  self-evident,  and  such  that  it  is  impossible  by  reason- 
ing to  make  it  plainer  ;  because  there  is  no  truth  more 
obvious,  or  better  known,  from  which,  as  a  consequence 
it  may  be  deduced.  But  if  we  say,  this  world  had  a  be- 
ginning ;  the  assertion  is  indeed  equally  true,  but  shines 
not  forth  with  the  same  degree  of  evidence.  We  find 
great  difficulty  in  conceiving  how  the  world  could  be  * 
made  out  of  nothing  ;  and  are  not  brought  to  a  free 
and  full  consent,  until  by  reasoning  we  arrive  at  a  clear 
view  of  the  absurdity  involved  in  the  contrary  supposi- 
tion. Hence  this,  proposition  is  of  the  kind  we  call 
demonstrable,  inasmuch  as  its  truth  is  not  immediately 
perceived  by  the  mind,  but  yet  may  be  made  appear  by 
means  of  others  more  known  and  obvious,  whence  it 
follows  as  an  unavoidable  consequence. 

Sec.  IlL.vJFA?  the  second  operation  of  the   Mind  is 
.  confined  wholly  to  Intuition* 

From  what  has  been  said,  it  appears  that  reasoning 
is  employed  only  about  demonstrable'  propositions,  and 
that  our  intuitive  and  self-evident  perceptions  are  the 
ultimate  foundation  on  which  it  rests.  And  now  we 
see  clearly  the  reason,  why  in  the  distinction  of  the 
powers  of  the  understanding,  as  explained  in  the  in- 
troduction to  the  treatise;  the  second  operation  of  the; 


120         DUNCAN'S  ELEMENTS 

mind  was  confined  wholly  to  intuitive  acts.  Our  first 
step,  in  the  way  to  knowledge,  is  to  furnish  ourselves 
with  ideas.  When  these  are  obtained,  we  next  set  our- 
selves to  compare  them  together,  in  order  to  judge  o£ 
their  agreement  or  disagreement.  If  the  relations  we 
are  in  quest  of,  lie  immediately  open  to  the  view  of  the 
mind,  the  judgments  expressing  them  are  self  evident ; 
and  the  act  of  the  mind,  forming  these  judgments,  is 
what  we  call  intuition.  But  if,  upon  comparing  our 
ideas  together,  we  cannot  readily  and  at  once  trace 
their  relation,  it  then  becomes  necessary  to  employ 
search  and  examination,  and  call  in  the  assistance  of 
self-evident  truths,  which  is  what  we  properly  term 
reasoning.  Every  judgment,  therefore,  that  is  not  in- 
tuitive, being  gained  by  an  exercise  of  the  reasoning 
faculty,  necessarily  belongs  to  the  third  operation  of 
the  mind,  and  ought  to  be  referred  to  it  in  a  just  divi- 
sion of  the  powers  of  the  understanding.  And  indeed, 
it  is  with  this  view  chiefly,  that  wTe  have  distinguished 
propositions  into  self-evident  and  demonstrable.  Un- 
der the  first  head  are  comprehended  all  our  intuitive 
judgments,  that  is,  all  belonged  to  the  second  opera- 
tion of  the  mind.  Demonstrable  propositions  are  the 
proper  province  of  the  reasoning  faculty,  and  consti- 
tute by  far  the  most  considerable  part  of  human  know- 
ledge. Indeed  reason  extends  also  to  matters  of  expe- 
rience and  testimony^  where  the  proofs  adduced  are  not 
of  the  kind  called  demonstration.  But  I  am  here  only 
considering  the  powers  of  the  mind  as  employed  in  tra- 
cing the  relations  between  its  own  ideas,  in  which 
view  of  things,  every  true  proposition  is  demonstrable  ; 
though  very  often  we  find  ourselves  incapable  of  disco- 
vering and  applying  those  intermediate  ideas  upon 
which  the  demonstration  depends. 

Sec.  IV '....Self-evident  Truths  the  Jirst  Principles  of 
Reasoning. 

Demonstrable  propositions,  therefore-,  belonging  pro- 
perly to  the  third  operation  of  the  mind,  I  shall,  for 
the  present,  dismiss  them,  and  return  to  the  consider^ 
atioa  of  self-evident  truths*     These  as  I  have  already 


OF  LOGIC.  121 

observed,  furnish  the  first  principles  of  reasoning  ;  and 
it  is  certain,  that  if  in  our  researches,  we  employ  only 
such  principles  as  have  this  character  of  self-evidence, 
and  apply  them  according  to  the  rules  to  be  after- 
wards explained,  we  shall  be  in  no  danger  of  error,  in 
advancing  from  one  discovery  to  another.  For  this  I 
may  appeal  to  the  writings  of  the  mathematicians, 
which,  being  conducted  by  the  express  model  here 
mentioned,  are  an  incontestable  proof  of  the  firmness 
and  stability  of  human  knowledge,  when  built  upon  so 
sure  a  foundation.  For  not  only  have  the  propositions 
of  this  science  stood  the  test  of  ages,  but  are  found 
attended  with  such  invincible  evidence,  as  forces  the 
assent  of  all  who  duly  consider  the  proofs  upon  which 
they  are  established.  Since  then  mathematicians  are 
universally  allowed  to  have  hit  .upon  the  right  method 
of  arriving  at  truths— -since  they  have  been  the  hap- 
piest in  the  choice,  as  well  as  application  of  their  prin- 
ciples— it  may  not  be  amiss  .to  explain  here  the  divi- 
sion they  have  given  of  self-evident  propositions  ;  that, 
by  treading  in  their  steps,  we  may  learn  something  of 
that  justness  and  solidity  of  reasoning,  for  which  they 
are  so  deservedly  esteemed. 

Sec.  V Definitions  a  great  help  to  Clearess  andEvi* 

dence  in  Knowledge. 

First,  then  it  is  to  be  observed,  that  they  have  been 
very  careful  in  ascertaining  their  ideas,  and  fixing  the 
significations  of  their  terms.  For  vhis  purpose  they 
begin  with  definitions,  in  which  the  meaning  of  their 
words  is  so  distinctly  explained,  that  they  cannot  fail 
to  excite  in  the  mind  of  an  attentive  reader  the  very 
same  ideas  as  are  annexed  to  them  by  the  writer.  And 
indeed  I  am  apt  to  think,  that  the  clearness  and  irre- 
sistible evidence  of  mathematical  knowledge,  is  owing 
to  nothing  so  much  as  this  care  in  laying  the  founda- 
tion. Where  the  relation  between  any  two  ideas  is 
accurately  and  justly  traced,  it  will  not  be  difficult  for 
another  to  comprehend  that  relation,  if  insetting  him- 
self to  discover  it,  he  brings  the  very  same  ideas  into 
•comparison.     But  if,  on  the  contrary,  he  affixes  to  his 


122  DUNCAN'S  ELEMENTS 

■words  ideas  different  from  those  that  were  in  the  mind 
of  him  who  first  advanced  the  demonstration  ;  it  is 
evident,  that  as  the  same  ideas  are  not  compared,  the 
same  relation  cannot  subsist,  insomuch  that  a  proposi- 
tion will  be  rejected  as  false,-  which  had  the  terms  been 
rightly  understood,  must  have  appeared  unexception- 
ably  true,  A  square, vfor  instance,  is  a  figure  bounded 
by  four  equal  right  lines,  joined  together  at  right  an- 
gles. Here  the  nature  of  the  angles  makes  no  less  a 
part  of  the  idea,  than  the  equality  of  the  sides  ;  and 
many  properties,  demonstrated  of  the  square,  flow  from 
its  being  a  rectangular  figure.  If,  therefore,  we  sup- 
pose a  man  who  has  formed  a  partial  notion  of  a  square, 
comprehending  only  the  quality  of  its  sides,  without 
regard  to  the  angles,  reading  some,  demonstration  that 
implies  also  this  latter  Consideration  ;  it  is  plain  he 
would  reject  it  as  not  universally  true,  inasmuch  as  it 
could  not  be  applied  where  the  sides  were  joined  to- 
gether at  unequal  angles.  For  this  last  figure,  answer- 
ing still  to  his  idea  of  a  square,  would  be  yet  found 
without  the  property  assigned  to  it  in  the  proposition. 
But  if  he  comes  afterwards  to  correct  his  notion,  and 
render  his  idea  complete,  he  will  then  readily  own  the 
truth  and  justness  of  the  demonstration. 

Sec.  VI.... Mathematicians  by  beginning  with  them,  pro* 
cure  a  ready  reception  to  the  truths  they  advaTice* 

We  see,  therefore,  that  nothing  contributes  so  much 
to  the  improvement  and  certainty  of  human  know- 
ledge, as  the  having  determinate  ideas,  and  keeping 
them  steady  and  invariable  in  all  our  discourses  and 
reasonings  about  them.  And  on  this  account  it  is,  that 
mathematicians,  as  was  before  observed,  always  begin 
by  defining  their  terms,  and  distinctly  unfolding  the 
notions  they  are  intended  to  express.  Hence  such  as 
apply  themselves  to  these  studies,  -  having  exactly  the 
same  views  of  things,  and  bringing  always  the  very 
same  ideas  into  comparison,  readily  discern  the  rela- 
tions between  them,  when  clearly  and  distinctly  repre- 
sented. Nor  is  there  any  more  natural  and  obvious 
reason  for  the  universal  reception  given  to  mathemati. 


OF  LOGIC.  123 

cal  truths,  and  for  that  harmony  and  correspondence 
of  sentiments  which  makes  the*  distinguishing  charac- 
ter of  the  literati  of  this  class. 

bee.   VII.... The  establishing  of  Principles  the  Second 
Step  in  Mat; hematic al Knowledge. 
When  the/  likve    taken  this   first   step,   and   made 
*  n  the  ideas,  whose  relations  they  intend  to  inves- 
tigate, their  next  care  is,  to  lay  down   some  self-evi- 
dent truths,    which    may    serve    as   a    foundation  for 
their  future  reasonings.      And  here; indeed,  they  pro- 
ceed with  remarkable    circumspection,    admitting    no 
principles"  bui:  what  flow  immediately  from  their  defini- 
tions, and  necessarily  force  themselves  upon  a  mind  in 
any  degree  attentive  to  its  precoptioOK      Thus  a  cir- 
cle is  a   figure  formed*  by  a  right  line,    moving  round 
some  fixed  point  in  the  same  plane.     The  fixed  point, 
round  which  the  line  is  supposed  to   move,  and  where 
one  of  its  extremities  terminates,  is  called  the  centre 
*f  the  circle.     The  other  extremity,  which  is  conceiv- 
carried  round,  until   it  returns   to  the  point 
wlu  out,  describes  a  curve  running  into 

itself,  and  termed  the  circumference.  All  right  lines, 
drawn  from  the  centre  to  the  circumference,  are  called 
radii.  From-  these  definitions  compared,  geometrici- 
ans derive  this  self-evident  truth,  that  the  radii  of  the 
same  circle  are  all  equal  one  to  another.  I  call  it  self- 
evident,  because  nothing  more  is  required,  to.  lay  it 
open  to  the  immediate  preception  of  the  mind,  than  an 
attention. to  the  ideas. compared.  For  from  the  very 
nature  of  a  circle  it  is  plain,  that  the  circumference  is 
every  where  distant  from  the  centre,  by  the'  exact 
length  of  the  describing  line  ;  and  that  the  several  ra- 
dii are  in  truth  nothing  more,  than  one  and  the  same 
line  variously  posited  within  the  figure.  This  short 
.  ription  will,  -I  hope,  serve  to  give  some  little  in- 
sight into  fche  manner  of  deducing  mathematical  prin- 
ciples, as  v.  til  as  into  the  nature  of  that  evidence 
which  accompanies  them* 

Sec.  V ill. ...Propositions  divided  into  Speculative  and 
Practical. 
And  now  I  proceed  to  observe,  that  in  all  proppsU 


124  DUNCAN'S  ELEMENTS 

tions  we  cither  affirm  or  deny  some  property  of  the 
idea  that  constitutes  the  subject  of  our  judgment,  of 
v/c  maintain  that  something  may  be  done  or  effected. 
The  first  sort  is  called  speculative  propositions,  as  in 
the  example  mentioned  above,  the  radii  of  the  same 
tircle  ore  all  equal  one  to  another.  The  others  are  cal- 
led practical^  for  a  reason  too  obvious  to  be  mention- 
ed; thus,  that  a  right  line  maybe  drawn  from  one 
point  to  another,  is  a  practical  proposition  ;  inasmuch 
as  it  expresses  that  something  may  be  done. 

Sec.  lX....i/iwe  Mathematical  Principles  distinguish* 
ed  into  Axioms  find  Postulates* 

From  this  twofold  consideration  of  propositions,  ari- 
ses the  twofold  division  of  mathematical  principles, 
into  axioms  and  postulates.  By  an  axiom  they  under- 
stand any  self-evident  speculative  truth :  as,  that  the 
whole  is  greater  than  its  parts  :  that  things  equal  to 
tne  and  the  same  thing,  are  equal  to  one  another.  But 
a  self-evident  practical  proposition  is  what  they  call  a 
postulate.  Such  are  these  of  Euclid  ;  that  a  finite  right 
line  maybe  continued  directly  forwards:  that  a  circle  may 
be  described  about  any  centre  with  any  distance.  And 
here  we  are  to  observe,  that  as  in  an  axiom,  the 
agreemeet  or  disagreement  between  the  subject  and 
predicate,  must  come  under  the  immediate  inspection 
of  the  mind;  so  in  a  postulate,  not  only  the  possibility 
of  the  thing  asserted  must  be  evident  at  first  view,  but 
also  the  manner  in  which  it  may  be  effected.  But 
•where  this  manner  is  not  of  itself  apparent,  the  propo- 
sition comes  under  the  notion  of  the  demonstrable  kind, 
and  is  treated  as  such  by  the  geometrical  writers. 
Thus,  to  draw  a  line  from  one  point  to  another,  is  as- 
sumed by  Euclid  as  a  postulate,  because  the  manner  of 
doing  it  is  so  obvious,  as  to  require  no  previous  teach- 
ing. But  then  it  is  not  equally  evident,  how  we  art 
to  construct  an  equilateral  triangle.  For  this  reason  he 
advances  it  as  a  demonstrable  proposition,  lays  down 
rules  for  the  exact  performance,  and  at  the  same  time 
proves,  that  if  these  rules  are  followed,  the  figure  will 
be  justly  described. 


OF  LOGIC.  125 

Sec.  X;..And  demonstrable  Propositions  into  Theo- 
rems and  Problems. 
This  naturally  leads  me  to  take  notice,  that  as  self- 
evident  truths  are  distinguished  into  different  kinds,  ac- 
cording asthey  are  speculative  or  practical  ;  so  is  it  al- 
so with  demonstrable  propositions.  A  demonstrable  spe- 
culative proposition  is  by;  mathematicians  called  a  theo- 
rem. Such  is  the  famous  47th  proposition  of  the  first 
book  of  the  Elements,  known  by  the  name  of  the  Pytha- 
gor'ic  theorem,  from  its  supposed  inventor,  Pythagoras, 
viz.  That  in  every  right-angled  triangle,  the  square  des- 
cribed upon  the  side  subtending  the  right  angle,  is  equal 
to  both  the  squares  described  upon  the  sides  containing 
the  right  angle.  On  the  other  hand,  a  demonstrable  prac- 
tical proposition  is  called  a  problem  ;  as  where  Euclid 
teaches  us  to  describe  a  square,  upon  a  given  right  line* 

Sec.  XI. ...Corollaries  are  obvious  adductions  from  The- 
orems or  Problems. 
Since  I  am  upon  this  subject,  it  may  not  be  amiss  to 
add,  that  besides  the  four  kinds  of  propositions  already 
mentioned,  mathematicians  have  also  a  fifth,  known  by 
the  name  of  corollaries.  These  are  usually  subjoined  to 
theorems  ov  problems,  and  differ  f&om  them  only  in  this, 
that  they  flow  from  what  is  there  demonstrated,  in  so 
obvious  a  maimer  as  to  discover'  tkeir  dependence  upon 
the  proposition  whence  they  are  deduced,  almost  as  sopn 
as  proposed.  Thus  Euclid  having  demonstrated,  that  in 
every  right-lined  triangle.,  all  the  three  angles  taken  toge- 
ther are  equal  to  two  rigli£  angles  ;  adds,  by  way  of  co- 
rollary, that  all  the  three  angles  of  any  one  triangle  take% 
together,  are  equal  to  all  the  three  angles  of  any  other 
triangle,  taken  together  :  which  is  evident  at  first  sight; 
because  in  all  cases  they  are  equal  to  two  right  ones, 
and  things  equal  to  two  and  the  same  thing,  are  equal 
to  one  another. 

Sec.  XII.,..  Scholia  serves  the  purposes  of  Annotations 

or  a  Comment. 

The  last  thing  I  shall  take  notice  of,  in  the  practice 

of  the  mathematicians,  is  what  they  call  their  scholia* 

They  are  indifferently  annexed  to  dsfmitionsj  proposi- 

L  2 


126  DUNCAN'S  ELEMENTS 

tions,  or  corollaries  ;  and  answer  the  same  purposes  Is 
annotations  upon  a  classic  author.  For  in  them  occasion 
is  taken,  to  explain  whatever  may  appear  intricate  and 
obscure  in  a  train  of  reasoning  ;  to  answer  objections  ; 
to  teach  the  application  and  uses  of  propositions  ;  to 
lay  open  the  original  and  history  of  the  several  disco- 
veries  made  in  the  science  ;  and  in  a  word,  to  acquaint 
us  with  all  such  particulars  as  deserve  to  be  known, 
whether  considered  as  points  of  curiosity  or  profit. 

Sec.    XIII This   Method    of  the   Mathematicians 

universal^  and  a  sure  guide  to  Certainty* 
Thus  we  have  taken  a  short  view  of  the  so  much 
celebrated  method  of  the  mathematicians ;  which,  to 
any  one  who  considers  it  with  a  proper  attention,  must 
needs  appear  universal,  and  equally  applicable  in  other 
sciences.  They  begin  with  definitions.  From,  these 
they  deduce  their  axioms  and  postulates,  which  serve 
as  principles  of  reasoning  ;  aud  having  thus  laid  a  firm 
foundation,  advance  to  theorems  and  problems,  esta- 
blishing all  by  the  strictest  rules  of  demonstration.  The 
corollaries  flow  naturally  and  of  themselves.  And  if 
any  particulars  are  still  wanting  to  illustrate  a  subject, 
or  complete  the  reader's  information  ;  these,  that  the 
series  of  reasoning  may  not  be  interrupted  or  broken, 
are  generally  thrown  into  scholia.  In  a  system  of 
knowledge  so  uniform  and  well  connected,  no  wonder 
if  we  meet  with  certainty ;  and  if  those  clouds  and 
darknesses,  that  deface  other  parts  of  human  science, 
and  bring  discredit  even  upon  reason  itself,  are  here 
scattered  and  disappear. 

Sec.  XIV ....Self  evident  Truths  known  by  the  appa- 
rent unavoidable  Connection  between  the  Subject  and 
Predicate. 

But  I  shall  for  the  present  wave  these  reflexions, 
•which  every  reader  of  understanding  is  able  to  make 
of  himself,  and  return  to  the  consideration  of  self-evi- 
dent propositions.  It  will,  doubtless,  be  expected,  af- 
ter what  has  been  here  said  of  them,  that  I  should 
establish  some  criteria^  or  marks,  by  which  they  may 
fcc  distinguished.    But  I  frankly  own  my  inability  in 


OF  LOGIC.  127 

this  respect,  m  not  being  able  to  conceive  any  thing  in 
them  more  obvious  and  striking,  than  that  self-evidence 
which  constitutes  their  very  nature.  All  I  have  there- 
fore to  observe  on  this  head,  is,  that  we  ought  to  make 
it  our  first  care,  to  obtain  clear  and  determinate  ideas. 
When  afterwards  we  come  to  compare  these  together, 
if  we  perceive  between  any  of  them  a  necessary  and 
unavoidable  connection,  insomuch  that  it  is  impossible 
to  conceive  them  existing  asunder,  without  destroying 
the  very  ideas  compared  ;  we  may  then  conclude,  that 
the  proposition  expressing  this  relation  is  a  principle, 
and  of  the  kind  we  call  self-evident.  In  the  example 
mentioned  above,  the  radii  of  the  same  circle  are  all 
equal  between  themselves,  this  intuitive  evidence  shines 
forth  in  the  clearest  manner  ;  it  Ugjng  impossible  for 
any  one,  who  attends  his  own  ideas,  nit  to  perceive  the 
equality  here  asserted.  For  as  tlie  circumference  it 
every  where  distant  from  the  centre  by  the  exact 
length  of  th>  describing  line  ;  the  radii  drawn  from 
the  centre  of  the  circumference,  being  severally  equal 
to  this  one  line,  must  needs  also  be  equal  among  them- 
selves.  If  we  suppose  the  radii  unequal,  we  at  the  same 
time  suppose  the  circumference  more  distant  from  the 
centre  in  some  places  than  in  others  ;  from  whichsup- 
position,  as  it  would  exhibit  a  figure  quite  different 
from  a  circle,  we  see  there  is  no  separating  the  predi- 
cate from  the  subject  in  this  proposition,  without  de- 
stroying the  idea  in  relation  to  which  the  comparison 
was  made.  The  same  thing  will  be  found  to  hold  in 
all  our  other  intuitive  perceptions,  insomuch  that  we 
may  establish  this  as  an  universal  criterion^  whereby 
to  judge  of,  and  distinguish  them.  I  would  not,  how- 
ever, be  understood  to  mean,  as  if  this  ready  view  of 
the  unavoidable  connection  between  some  ideas  was 
any  thing  really  different  from  self-evidence.  It  is, 
indeed,  nothing  more  than  the  notion  of  self-evidence? 
si  little  unfolded,  and  as  it  were  laid  open  to  the  inspec- 
tion of  the  mind.  Intuitive  judgments  need  no  other 
distinguishing  marks,  than  that  brightness  which  sur- 
rounds them  ;  in  like  manner  as  light  discovers  itself 
by  its  owe  f resence;  and   the  splendor  it  universally 


128  DUNCAN'S  ELEMENTS 


^s.     But  I  have  said  enough  of  self-evident  pro- 
''   lis,  and  shall  therefore  now  proceed  to  those  of 


diffuses. 

'positions,  and  shall  therefore  now  proceed  to  those  of 
the  demonstrable  kind;  which,  being  gained  in  conse- 
quence of  reasoning,  naturally  leads  us  to  the  third 
part  of  logic^wliere  this  operation  of  the  understanding 
is  explained. 


IJOOK  III. 


V--Ttt 


OF    REASONING. 


tRbap*'  1. 


OF  REASONING  IN  GENERAL,  AND  THE 
PARTS  OF  WHICH  IT  CONSISTS. 


Sec,  \..,*Remote  Relations  discovered  by  means  of  in* 

termediate  Ideas. 

Wl 
E  have  seen  how  the  mind  proceeds  in  furnish- 
ing itself  with  ideas,  and  framing  intuitive 
perceptions.  Let  us  next  enquire  into  the  manner  o£ 
discovering  those  more  remote  relations,  which,  lying 
at  a  distance  from  the  understanding,  are  not  to  be 
traced  but  by  means  of  a  higher  exercise  of  its  powers. 
It  often  happens  in  comparing  ideas  together,  that 
their  agreement for.  disagreement. cannot  be  discerned 
at  first  view,  especially  if  they  are  of  such  a  nature,  as 
not  to  admit  of  an  exact  application  one  to  another. 
When,  for  instance,  we  compare  two  figures  of  a  dif- 
ferent make,  in  order  to  judge  of  their  equality  or  in- 
equality, it  is  plain,  that  by  barely  considering  the  £• 


OF  LOGIC.  129 

jure*  themselves,  we  cannot  arrive  at  an  exact  deter- 
mination  ;  because,  by  reason  of  their  disagreeing 
forms,  it  is  impossible  so  to  put  them  together,  as  that 
their  several  parts  shall  mutually  coincide.  Here  the» 
it  becomes  necessary  to  look  out  for  some  third  ideaf 
i  that  will  admit  of  such  an  application  as  the  present 
•ase  requires  ;  wherein  if  we  succeed,  all  difficulties 
vanish,  and  the  relation  we  are  in  quest  of  may  be 
traced  with  ease.  Thus  right-lined  figures  are  all  re- 
ducible to  squares,  by  means  of  which  we  can  measure 
their  areas,  and  determine  exactly  their  agreement  or 
disagreement  in  point  of  magnitude. 

Sec.  II....  jT^/j  manner  of  arriving  at  Truth  andterm* 
ed  Reasoning. 
If  now  it  be  asked,  how  any  third  idea  can  serve  t# 
discover  a  relation  between  two  others  ;  I  answerf 
by  being  compared  severally  with  these  others  ;  for 
such  a  comparison  enables  us  to  see  how  far  the  ideasf 
with  which  this  third  is  compared,  are  connected  or 
disjoined  between  themselves.  In  the  example  men* 
tioned  above,  of  two  right-lined  figures,  if  we  com- 
pare each  of  them  with  some  square  whose  area  il 
known,  and  find  the  one  exactly  equal  to  it,  and  the 
other  less  by  a  square-inch  greai-t  than  that  of  the  se- 
cond. This  manner  of  determining  the  relation  be- 
tween any  two  ideas,  by  the  invention  of  some  third 
with  which  they  may  be  compared,  is  that  which  we 
call  reasoning,  and  indeed  the  chief  instrument,  by 
which  we  push  on  our  discoveries,  and  enlarge  our 
knowledge.  The  great  art  lies,  in  finding  out  such  in- 
termediate ideas,  a3,  when  compared  with  the  others 
in  the  question,  will  furnish  evident  and  known  truths  ; 
because,  as  will  afterwards  appear,  it  is  only  by  means 
of  them,  that  we  arrive  at  the  knowledge  of  what  is 
Jaidden  and  remote. 

Sec.  III. ...  The  parts  that  constitute  an  Act  of  Reason* 
ing  and  a  Syllogism, 
From  what  has  been  said,  it  appears  that  every  act 
of  reasoning  necessarily  includes  three  distinct  judg- 
ments j  two,  wherein   tbe  ideas,  whose   relatign  trfc 


130  DUNCAN'S  ELEMENTS 

"want  to  discover,  are  severally  compared  with,  the  mid- 
^dieidea,  and  a  third,  wherein  they  are  themselves  con- 
nected or  disjoined  according  to  the  result  of  that  com- 
parison. Now  as  in  the  second  part  of  logic,  our 
judgments  when  put  into  words,  were  called  proposi- 
tions....so  here,  in  the  third  part, the  expressions,  of  our 
t  reasonings  are  termed  syllogisms.  And  hence  it  fol- 
lows, that  as  every  act  of  reasoning  implies  three  se- 
veral judgments,  so  every  syllogism  must  include  three 
distinct  propositions.  When  a  reasoning  is  thus  pil-t 
into  words,  and  appears  in  form  of  a  syllogism,  the 
intermediate  ideat  made  use  of  to  discover  the  agree- 
ment or  disagreement  we  search  for,  is  called  the  mid- 
dle term  ;  and  the  two  ideas  themselves,  with  which 
this  third  is  compared/ go  by  the  name  of  the  extremes. 

Sec.  IV, ...Instance,   Man  and  Accountableness. 

But  as  these  things  are  best  illustrated  by  examples  ; 
•let  us,  for  instance,  set  ourselves  to  enquire,  whether 
men  are  accountable  for  their  actions.  As  the  relation 
•between  the  ideas  of  man  and  account  alien  ess  Route's 
not  within  the  immediate  view  of  the  mind,  our  fhst 
care  must  be,  to  find  out  some  third  idea,  that  will  ena- 
ble us  the  more  easily  to  discover  and  trace  it.  A  very 
small  measure  of  rerlexionis  sufficient  to.  infirm  us, 
that  no  creature  can  be  accountable  for  his  actions,  un- 
less we  suppose  him  capable  of  distinguishing  the' good 
from  the  bad  ;  that  is  unless  we  suppose  him  -posst 
of  reason.  Nor  is  this  alone  suiticient.  For  .what 
"would  it  avail  him,  to  know  gobd  \  actions,  if  he 

-had  no  freedom  of  choice,  nor  could  avoid  the  o.^e,  and 
pursue  the  other  ?    Hence  it  o'efcomes  necessary  to  I 
in  both  considerations  in  the  presenVense.      It  is  fit 
same  time  equally  apparent,  that  wherever  there  is  'this 
ability  of  distinguishing  good  from  bad  action?. 
suing  the  one  and  avoiding  the  other,'  there  "also  a  - 
ture  is  accountable.      We, have  then  got  a  xy. 
"with  which  account a^icness  is  inseparably  connected,  viz. 
reason  and  liberty ;  which  are  here  to-be  considered  as 
making  up.  one  complex  conception.     Let  us  now  take 
this  middle  idea,  and  compare  it  with  tlw  otkw  fW  i* 


OF  LOGIC.  1st 

the  question,  viz.  man,  and  we  all  know  by  experience 
that  it  may  be  affirmed  of  him.  Having  thus,  by  means 
of  the  intermediate  idea,  formed  two  several  judgments, 
viz.  that  man  is  possessedof  reason  and  liberty  ;  and  that 
reason  and  liberty  imply  accountableness  ;  a  third  obvious- 
ly and  necessarily  follows,  viz.  that  man  is  accountable 
for  his  actions.  Here  then  we  have  a  complete  act  of  rea- 
soning, Id  which,  according  to  what  has  been  already- 
observed,  there  are  three  distinct  judgments  ;  two  that 
may  be  stiled  previous,  inasmuch' as  they  lead  to  the 
other,  and  arise  from  comparing  the  middle  idea  with 
the  two  ideas  in  the  question ;  the  third  is  a  consequence 
of  these  previous  acts,  and  flows  from  combining  the  ex- 
treme ideas  between  themselves.  If  i\ow  we  put  this  rea- 
soning into  words,  it  exhibits  what  logicians  term  a  syl* 
logism,  and,  when  proposed  in  due  form,  runs  thus  : 

Every  creature  possessed  of  reason  and  liberty  is  account** 
•ble  for  his  actions. 
.    Man  is  a  creature  possessed  of  reason  and  liberty. 

Therefore  man  is  accountable  forh,is  actions. 

Sec,  V.... Premises,  conclusion,  extremes,  middle  term* 
In  this  syllogism  we  may  observe,  that  there  are  three 
several  propositions,  expressing  the  three  judgments 
implied  in  the  act  of  reasoning,  and  so  disposed  as  to 
represent  distinctly  what  passes  within  the  mind,  in 
tracing  the  more  distant  relations  of  its  ideas.  The  two 
first  propositions  answer  the  two  previous  judgments  in 
reasoning,  and  are  called  the  premises,  because  they 
are  placed  before  the  other.  The  third  is  termed  the 
conclusion,  as  being  gained  in  consequence  of  what  was 
asserted  in  the  premises.  We  are  also  to  remember, 
that  the  terms  expressing  the  two  ideas  whose  relation 
we  enquire  after,  as  here  man  and  accountableness,  are  in 
general,  called  the  extremes;  and  that  the  intermediate 
idea,  by  means  of  which,  the  relation  is  traced,  viz.  a  crea~ 
ture  possessed  of  reason  and  liberty,  takes  the  name 
of  the  middle  term*  Hence  it  follows,  that  by  Xhepre* 
raises  of  a  syllogism,  we  are  always  to  understand  the 
two  propositions,-  where  the  middle  term  is  severally* 
compared  with  extremes  ;  for  these  constitute  the  pre- 
vious judgments,  whence  the  truth  we  are  in  quest  of 


l$2         DUNCAN'S  ELEMENTS 

li  by  reasoning  deduced.  The  conclusion  is  that  ether 
proposition,  in  which  the  extremes  themselves  are 
joined  or  separated,  agreeably  to  what  appears  upon  the 
above  comparison.  All  this  is  evidently  seen  in  the  fore- 
going syllogism,  where  the  two  first  propositions,  which 
represent  the  premises,  and  the  third,  which  makes  the 
conclusion,  are  exactly  agreeable  to  the  definitions  here 
given. 

Sec  VI.... Major  and  Minor  Termy  Major  and  Minor 
Proposition* 

Before  we  take  leave  of  this  article,  it  will  be  far- 
ther necessary  to  observe,   that  as   the  conclusion  is 
made   up  of  the  extreme    terms  of  the  syllogism  ;  so 
that  extreme,  which  serves  as  the  predicate  of  the  con* 
elusion,   goes  by  the   name  of  the    major  term :  the 
other  extreme,   which  makes   the  subject  in  the  same 
proposition,  is  called  the  minor  term.     From  this  dis- 
tinction of  the  extremes,  arises  also  a  distinction  be- 
tween the  premises,  where  these  extremes  are  several- 
ly compared  with  the  middle  term.     That  proposition, 
which  compares  the  greater  extreme,  or  the  predicate 
of  the  conclusion,  with  the  middle  term,  is  called  the 
major  proposition  :  the  other,    wherein  the  same  mid- 
dle term  is  compared  with   the  subject  of  the  conclu- 
sion, or  lesser  extreme,  is  called  tne  minor  proposition. 
All  this    is  obvious  from  the  syllogism  already  given, 
where  the  conclusion  is,  man  is  accountable  for  his  ac- 
tions.      For  here    the   predicate,    accountable  for  his 
actions,  bsing  connected  with  the  middle  term  in  the 
first  of  the  two  premises.     Every  creature  possessed  of 
reason  and  liberty  is  accountable  for  his  actions,  gives 
what  we  sail  the  major  proposition.     In  the  second  of 
the  premises,  man,  is  a  creature  possessed  of  reason  and 
liberty,  we  find  the  lesser  extreme,  or  subject,  of  the 
conclusion,  viz.  man,  connected  with  the  same  middle 
term,  whence  it  is  known  to  be  the  minor  proposition* 
I  shall  only  add,  that  when  a  syllogism  is  proposed  in 
-due  form,  the  major  proposition   is  always  placed  first, 
the  minor  next,  and  the  conclusion  last,  according  aa 
wc  have  done  in  tkat  offered  abovct 


OF  LOGIC.  133 

S^c.    VII..,  •Judgment   and    Proposition,     Reasoning 
and  Syllogism  distinguished. 
Having  thus    cleared   the  way,  by  explaining. suck 
terms,  as  we  are  likely  to  have  occasion  for  in  the  pro- 
gress of  this  treatise  ;  it  may  not  be  amiss  to  observe,     . 
that  tho'  we  have  carefully  distinguished  between  the 
act    of  reasoning,  and  a  syllogisjn,  which   is  no  more 
than  the  expression  of  it,  yet  common  language  is  not 
so   critical    on  this  head  ;  the  term   reasoning  being 
promiscuously   used,  to   signify  either  the  judgments 
of  the    mind,  as    they  follow   one    another  in  train, 
or     the    propositions     expressing     these    judgments. 
Nor  need   we  wonder  that  it  is  so,  inasmuch  as  our  • 
ideas,  and  the  terras  appropriated  to  them,  are  so  con- 
nected   by  habit  and  use,  that  our  thoughts  fall  as  it 
were   spontaneously   into  language,   as    fast   as   they 
arise  in  the   mind  ;  so    that  even   in  our  reasonings 
within  ourselves,  ve  are  not  able  wholly  to  lay  aside.  - 
words.      But  notwithstanding  this  strict  connexion  be- 
tween mental  and  verbal  reasoning,  if  I  maybe  allow- 
ed that  expression,   I  thought  it  needful  here  to  dis- 
tinguish them,  in  order  to  give  a  just  idea  of  the  man- 
ner of  deducing  one  truth  from  another.      While  the 
mind  keeps  the  ideas  of  things  in  view,  and  combines 
its  judgments  according  to  the  real  evidence  attending 
them,  there  is  no  great  danger  of  mistake  in  onr  rea- 
sonings ;  because  we  carry  our  conclusions  no  farther 
than  the  clearness    of  our   perceptions   warrants  us. 
But    where  we  make  use  of  words,  the   case  is  oftea 
otherwise  ;'  nothing  being  more  common,^  than  to  let 
them  pass  without  attending  to  the   ideas  they  repre- 
sent ;   insomuch  that  we  frequently  combine  expres- 
sions, which  upon  examination  appear  to  have  no  de? 
terminate  meaning.     Hence  it  greatly  imports  us.t© 
distinguish  between  reasoning  and  syllogism  ;    and  to 
take  care,  that  the  one  be  in  all  cases  the  true  and  just 
representation  of  the  other.      However,  as  I  am  un- 
willing to  recede  too  far  from  the  common  forms  of 
speech,  or  to  multiply  distinctions  without  necessity,  I 
shall  henceforward  consider  propositions  as  representing 
the  real  judgments  of  the  mind,  and  syllogisms  as  the 

M 


134         DUNCAN'S -ELEMENTS 

true  copies  of  our  reasonings  ;  which  indeed  they  ought 
always  to  be,  and  undoubtedly  always  will  be',' to  men 
■who  think  justly,  and  are  desirous  of  arriving  at  truth. 
Upon  this  supposition  there  will  be  no  danger  in  using 
the  words  judgment  and  proposition  promiscuously  ;  or 
in  considering  reasoning  as  either  a  combination  of  va- 
rious judgments,  or  of  the  propositions  expressing  them  ; 
because,  being  the  exact  copies  one  of  another,  the  re- 
sult will  be  in  all  cases  the  same.  Nor  is  it  a  small  ad- 
vantage, that  we  can  thus  conform  to  common  speech, 
without  confounding  our  ideas,  or  running  into  ambi- 
guity. By  this  means  we  bring  ourselves  upon  a  level 
with  other  men,  readily  apprehend  the  meaning  of  their 
expressions*,  and  can  with  ease  convey  our  own  notions 
•and  sentiments  into  their  minds. 

Sec.  VIII... ./«  a  single  Act  of  Reasonings  the  Premi- 
ses must  be  intuitive  Truths. 
These  things  premised,  we  may  in  the  general  define 
re*asoning  to  be  an  act  or  operation  of  t lie  mind,  dedu- 
cing some  unknown  proposition,  from  other  previous  ones 
that  are  evident  and  known.  These  previous  proposi- 
tions, in  a  simple  act  of  reasoning,  are  only  two  in 
number;  and  it  is  always  required  that  they  be  of 
themselves  apparent  to  the  understanding,  insomuch 
that  we  assent  to  and  perceive  the  truth  of  them  as 
soon  as  proposed.  In  the  syllogism  given  above,  the 
premises  are  supposed  to  be  self-evident  truths,  other- 
wise the  conclusion  could  not  be  inferred  by  a  single 
act  of  reasoning.  If,  for  instance,  in  the  major,  every 
creature  possessed  of  reason  and  liberty  is  accountable 
for.  his  actions,  the  connexion  between  the  subject  and 
predicate  could  not  be  perceived  by  a  bare  attention 
to  the  ideas  themselves  ;  it  is  evident,  that  this  propo- 
sition would  no  less  require  a  proof,  than  the  conclu- 
sion deduced  from  it.  In  this  case,  a  new  middle  term 
must  be  sought  for,  to  trace  the  connexion  here  sup- 
posed ;  and  this  of  course  furnishes  another  syllogism, 
by  which*  having  established  the  proposition  in  ques- 
tion, we  are  then,  and  not  before,  at  liberty  to  use  it 
in  any  succeeding  train  of  reasoning.  And  should  it 
so  happen,  that  in  this  second  essay,   there  was   still 


OF  LOGIC.  135 

some  previous  proposition  whose  truth  did  not  appear 
at  first  sight  ;  we  must  then  have  recourse  to  a  third 
syllogism,  in  order  to  lay  open  that  truth  to  the  mind  ; 
because  so  long*  as  the  premises  remain  uncertain,  the 
conclusion  built  upon  them  must  be  so  too.  When 
by  conducting  our  thoughts  in  this  manner,  we  at  last 
.  arrive  at  some  syllogism,  where  the  previous  proposi- 
tions are  intuitive  truths  ;  the  mind  then  rests  in  full 
security,  as  perceiving  that  the  several  conclusions  it 
has  passed  through,  stand  upon  the  immovable  found- 
ation of  self-evidence,  and,  when  traced  to  their 
source,  terminate  in  it. 

Sec.  IX.. ..Reasoning,  in  the   highest  Exercise    of  ;V, 
only  a  Concatenation  of  Syllogisms. 

We  see,  therefore,  that  in  order  to  infer  a  conclu- 
sion  by  a  single  act  of  reasoning,  the  premise?  must 
be  intuitive  propositions.  Where  they  are  not,  pre- 
vious syllogisms  are  required,,  in  which  case  reasoning 
becomes  a  complicated  act,  taking  in  a  variety  of  suc- 
cessive steps.  This  frequently  happens  in  tracing*  the 
more  remote  relations  of  our  ideas,  where  many  mid- 
dle terms  being  called  in,  the  conclusion  cannot  be 
made  out,  but  in  consequence-of  a  series  of  sy41ogi$m$ 
following  one  another  in  train.  But  although  in  this 
concatenation  of  propositions,  those  that  form  the  pre- 
-mises  of  the  last  syllogism,  are  often  considerably  re- 
moved from  self-evidence  ;  yet  if  we  trace  the  reason- 
ing backwards,  we  shall  find  them  the  conclusions  of 
/  previous  syllogisms,  whose  premises  approach  nearer 
and  nearer  to  intuition,  in  proportion  "as 'we  advance, 
and  are  found  at  last  to  terminate  in  it.  And  if  after 
having  thus  unravelled  a  demonstration,  we  take  it  the 
contrary  way,  and  observe  how  the  mind,  setting  out 
with  intuitive  perceptions,  couples  them  together  to 
form  a  conclusion — how,  by  introducing  this  conclu- 
sion into  another  syllogism,  it  still  advances  one  step 
farther  ;,and  so  proceeds,  making  every  new  discovery- 
subservient  to  its  future  progress. — we  shall  then  per- 
ceive clearly.,  that  reasoning,  in  the  highest  exercise 
of  that  faculty,   is  no  more  than  an  orderly  combina- 


136  DUNCAN'S  ELEMENTS 

tibn  of  those  simple  acts,  which  we  have  already  so 
fully  explained.  The  great  art  lies,  in  so  adjusting 
©ur  syllogisms  one  to  another,  that  the  propositions 
severally  made  use  of,  as  premises,  may  be  manifest 
consequences  of  what  goes  before."  For  as  by  this 
jaieaHS,  every  conclusion  is  deduced  from  known  and 
established  truths,  the  very  last  in  the  series,  how  far 
soever  we  carry  it,  will  have  no  less  certainty  attend- 
ing it,  .  than  the  original  intuitive  perceptions  then*-- 
selves,  in  which  the  whole  chain  of  syllogisms  takes  its 
rise. 

Sec.  X.... Requires  intuitive  Certainty  in  every  Step  of 
the  Progression. 
Thus  we -see,  that  reasoning,  beginning  with  first 
principles,  rises  gradually  from  one  judgment  to  ano- 
ther, and  connects  them  in  such  manner,  that  every 
stage  of  the  progression  brings  intuitive  certainty 
along  with  it.  And  now  at  length  we  may  clearly  un- 
derstand the  definition  given  above,  of  this  distinguish- 
ing faculty  of  the  human  mind.  Reason,  we  have  said, 
is  the  ability  of  deducing  unknown  truths,  from  prin- 
ciples or  propositions  that  are  already  known.  This 
evidently  appears,  by  the  foregoing  account,  where 
;  we  see,  that  no  proposition  is  admitted  into  a  syllo- 
gism, to  serve  as  one  of  the  previous  judgments  on 
which  the  conclusion  rests,  unless  it  is  itself  a  known 
and  established  truth,  whose  connexion  with  self-evi- 
dent principles  has  been  already  traced. 

Sec.  .XI ...  .Self-evident  Truths,  the  ultimate  Founda- 
tion of  all  Science  and  Certainty. 
There  is  yet  another  observation  which  naturally  of- 
fers itself,  in  consequence  of  the  above  detail  ;  viz. 
that  all  the  knowledge  acquired  by  reasoning,  how  far 
soever  we  carry  our  discoveries,  is  still  built  upon  our 
intuitive  perceptions.  Towards  the  end  of  the  last 
part,  we  .divided  propositions  into  self-evident  and  de- 
monstrable, and  represented  those  of  the  self-evident 
kind,  as  the  foundation- on  which  the  whole  super- 
structure of  human  science  rested.  _  Th'is  doctrine  is 
now  abundantly  confirmed  by  what  has  been  delivered 


OF  LOGIC.  1ST 

in  the  present  chapter.  We  have  found,  that  every 
discovery  of  human  reason,  is  the  consequence  of  a 
train  of  syllogisms,  which,  when  traced  to  their  source, 
always  terminate  in  self-evident  perceptions.  When 
the  mind  arrives  at  these  primitive  truths,  it  pursues 
not  its  enquiries  farther,  as  well  knowing,  that  no 
evidence  can  exceed  that  which  flows  from  an  imme- 
diate view  of  the  agreement  or  disagreement  between 
its  ideas.  And  hence  it  is,  that  in  unravelling  any  part 
of  knowledge,  in  order  to  come  at  the  foundation  on 
"which  it  stands  ;  intuitive  truths  are  always  the  last 
resort  of  the  understanding,  beyond  which  it  aims  not 
to  advance,  but  possesses  its  notions  in  perfect  security, 
as  having  now  reached  the  very  spring  and  fountain  of 
all  science  and  certainty. 

Cfjap.  IL 

OF  THE  SEVERAL  KINDS  OF  REASONING,  AND 
FIRST  OF  THAT  BY  WHICH  WE  DETERMINE 
THE  GENERA  AND  SPECIES  OF  THINGS. 

Sec.   I.... Reasoning  Twofold, 

WE  have  endeavoured,  in  the  foregoing  chapter, 
to  give  as  distinct  a  notion  as  possible,  of  rea- 
soning, and  of  the  manner  in  which  it  is  conducted.  Let 
us  now  enquire  a  little  into  the  discoveries  made  by 
this  faculty,  and  what  those  ends  are,  which  we  have 
principally  in  view  in  the  exercise  of  it.  All  the  aims 
of  human  reason  may^  in  the  general,  be  reduced*  to 
these  two  :  1.  To  rank  things  under  those  universal 
ideas  to  which  they  truly  belong  ;  and  2.  To  ascribe  to 
them  their  several  attributes  and  properties,  in  conse- 
quence of  that  distribution. 

Sec.   II.. ..The  first  kind  regards  the  Genera  and  Spe- 
cies of  Things. 
First,  then  I  say,  that  one  great  aim  of  human  rea- 
son is,  to  determine  the  genera  and  species  of  things. 
We   have  seen,  in  the^  first  part  of  this  treatise,  how 
.the  mind  proceeds  in  framing  general  ideas.     We  have 
also  seen,  ia  the  second  part,  how,  by  means  of  these 
M  2 


138  DUNCAN'S  ELEMENTS 

general  ideas,  we  come  by  universal  propositions.  Now 
as  in  these  universal  propositions,  we  affirm  some  pro- 
perty of  a  genus  or  species,  it  is  plain,  that  we  cannot 
apply  this  property  to  particular  objects,  till  we  have 
first,  determiued,  whether  they  are  comprehended  un- 
der that  general  idea,  of  which  the  property  is  affirm- 
ed. Thus  there  are  certain  properties  belonging  to  all 
even  numbers,  w+hich  nevertheless  cannot  be  applied  to 
any  particular  nurxber.  until  we  have  first  discovered 
it  to  be  of  the  species  expressed  by  that  general  name. 
Hence  reasoning  begins  with  referring  things  to  their 
several  divisions  and  classes  in  the  scale  of  our  ideas  ; 
and  as  these  divisions  are  all  distinguished  by  pe- 
culiar names,  we  hereby  learn  to  apply  the  terms  ex- 
pressing general  conceptions,  to  such  particular1  objects, 
as  come  under  our  immediate  observation. 

Sec.  IIIf.TJie  Steps  by  which  we   arrive  at  Conclu* 
sions  of  this  sort. 

Now  in  order  to  arrive  at  these  conclusions,  by  which 
ihe  several  objects  of  perceptions  are  brought  under 
general  names,  two  things  are  manifestly  necessary. 
Fiist,  that  we  take  a  view,  of  the  idea  itself  denoted  by 
that  general  name,  and  carefully  attend  to  the  distin- 
guishing marks  which  serve  to  characterize  it.  Se- 
condly, that  we  compare  this  idea  with  the  object  un- 
der consideration,  observing  diligently  wherein  they 
agree  or  differ.  If  the  idea  is  found  to  correspond 
with  the  particular  object,  we  then,  without  hesitation, 
apply  the  general  name  ;  but  if  no  such  correspondence 
intervenes,  the  conclusion  must  necessarily  take  a  con- 
trary turn.  Let  us,  for  instance,  take  the  number 
eight,  and  consider  by  what  steps  we  are  led  to  pro- 
nounce it  an  even  number.  First  then  we  call  to  mind 
•the  idea  signified  by  the  expression,  an  even  number^ 
viz.  that  it  is  a  number  divisible  into  two  equal  parts* 
We 'then  compare  this  idea  with  the  number  eight,  and 
finding  Jthem  manifestly  to  agree,  see  at  once  the  ne- 
cessity of  admitting  the  conclusion.  These  several 
judgments  therefore,  transferred  into  language,  and  rt» 
fUrctd  to  th«  fcr»  of  a  syilogUia;  appear  ikus  i 


OF  LOGIC.  130 

Every  number  that  may  be  divided  into  two  equal  parts* 
is  an  even  number 
The  number  eight  may  be  divided  into  two  equal  parts* 
Therefore  the  number  eight,  is  an  even  number. 

Sex  IV....  Those  steps  always  followed,  though    in  fa* 
miliar  cases  we  do  not  always  attend  to  them. 

'  I  have  made  choice  of  this  example,  not  so  much  for 
the  sake  of  the  conclusion,  which  is  obvious  enough 
and  might  have  been  obtained  without  all  that  parad© 
of  words  ;  but  chiefly  because  it  is  of  easy  compre- 
hension, and  serves,  at  the  same  time  distinctly  to  ex- 
hibit the  form  of  reasoning  by  which  the  understand- 
ing' conducts  itself  in  ,all  instances  of  this  kind.  >  And 
here  it  may  be  observed,  that  where  the  general  idea,  to 
which  particular  objects  are  referred,  is  very  familiar 
to  the  mind,  and  frequently"  in  view  ;  this  reference, 
and  the  application  of  the  general  name,  seem  to  be 
made  without  any  apparatus  of  reasoning.  When  we 
see  a  horse  in  the  fields,  or  a  dog  in  the  street,  we 
readily  apply  the  name  of  the  species  ;  habit,  and  a 
familiar  acquaintance  with  the  general  idea,  suggest- 
ing it  instantaneously  to  the  mind.  We  are  not, 
however,  to  imagine  on  this  account,  that  the  under- 
standing departs  from  the  usual  rules  of  just  thinking. 
A  frequent  repetition  of  acts  begets  a  habit ;  and  ha- 
bits are  attended  with  a  certain  promptness  of  execution, 
that  prevents  our  observing  the  several  steps  and  gra- 
dations, by  which  any  course  of  action  is  accomplish- 
ed. But  in  other  instances,  where  we  judge  not  by 
precontracted  habits,  as  when  the  general  idea  is  very 
complex,  or  less  familiar  to  the  mind  ;  we  always  pro- 
'ceed  according  to  the  form  of  reasoning  established 
above.  A  goldsmith,  for  instance,  who  is  in  doubt  as 
to  any  piece  of  metal,  whether  it  be  of  the  species  cal- 
led gold,  first  examines  its  properties,  and  then  com- 
paring them  with  the  general  idea  signified  by  that 
name,  if  he  find  a  perfect  correspondence,  no  longer 
hesitates  under  what  class  of  metals  to  rank  it.  Now 
what  is  this,  but  following  step  by  step  those  rules  ol 
reasoning,  which  we  have  before  laid  doirn  as  the  star>J: 


140  DUNCAN'S  ELEMENTS 

ards,  by  which  to  regulate  our  thoughts  in  all  conclu- 
sions of  this  kind  ? 

Sec.  V.....27j<?  Great  Importance  of  this  Branch  of 
Reasoning, 
Nor  let  be  imagined,  that  our  researches  here,  be- 
cause in  appearance  bounded  to  the  imposing  of  gene- 
ral names  upon  particular  objects,  are  therefore  trivi- 
al and  of  little  consequence.  Some  of  the  most  consi- 
derable debates  among  mankind,  and  such  too,  as1 
nearly  regard  their  lives,  interest,  and  happiness,  turn 
wholly  upon  this  article.  Is  it  not  the  chief  employ- 
ment of  our  several  courts  of  judicature,  to  determine, 
in  particular  instances,  what  is  law,  justice,  and  equi- 
ty ?  Of  what  importance  is  it,  in  many  cases,  to  decide 
aright,  whether  an  action  shall  be  termed  murder  or 
•manslaughter  ?  We  see,  that  no  less  than  the  lives  and 
fortunes  of  men  depend  often  upon  these  decisions. 
The  reason  is  plain.  Actions,  when  once  referred  to  a 
general  idea,  draw  after  them  all  that  may  be  affirmed 
of  that  idea  ;  insomuch  that  the  determining  the  species 
of  actions,  is  all  one  with  determining  what  proportion 
of  praise  or  dispraise,  commendation  or  blame,  &c. 
ought  to  follow  them.  For  as  it  is  allowed  that  murder 
deserves  death,  by  bringing  any  particular  action  under 
the  head  of  murder,  we  of  course  decide  the  punishment 
due  to  it. 

Sec.  VIm.i^  the  exact  observance  of  it  practised  by 
Mathematicians. 
*  But  the  great  importance  of  this  branch  of  reason- 
ing, and  the  necessity  of  care  and  circumspection,  in 
referring  particular  objects  to  general  ideas,  is  still  far- 
ther evident  from  the  practice  of  the  mathematicians. 
Every  one  who  has  read  Euclid,  knows,  that  he  fre- 
quently requires  us  to  draw  lines  through  certain  points, 
and  according'  to  such  and  such  directions.  The  fi- 
gures thence  resulting  are  often  squares,  parallelo- 
grams, or  rectangles.  Yet  Euclid  never  supposes  this 
from  their  bare  appearance,  but  always  demonstrates  it 
upon  the  strictest  principles  of  geometry.  Nor  is  the 
inethod  he  takes,  ia  any  thing  diffeixttt.fro;ni  that  des* 


OF  LOGIC.  141 ' 

eribed  above.  Thus,  for  instance,  having- defined  a 
square  to  be  a  figure  bounded  by  four  equal  sides,  join- 
ed together  at  right  angles  ;  when  such  a  figure  arises 
in  any  construction  previous  to  the  demonstration  of  a 
proposition,  he  yet  never  calls  it  by  that  name,  until  he 
has  shown  that  the  sides  are  equal,  and  all  its  angles 
right  ones.  Now  this  is  apparently  the  same  form  of 
reasoning  we  have  before  exhibited,  in  proving  eight  to 
be  an  even  number  ;  as  will  be  evident  to  any  one  who 
reduces  it  into  a  regular  syllogism.  I  shall  only  add, 
that  when  Euclid  has  thus  determined  the  species  of 
any  figure,  he  is  then,  and  not  before,  at  liberty  to  as- 
cribe to  it  all  the  properties  already  demonstrated  of 
that  figure,  and  thereby  render  it  subservient  to  the 
future  course  of  his  reasoning. 

Sec.  VII.,*.Fixed  and  invariable  Ideas,  with  a  steady 
application  of  Names,  renders  this  part  of  Know- 
ledge both  easy  and  certain. 

Having  thus  sufficiently  explained  the  rules  by  whick 
we  are  to  conduct  ourselves,  in  ranking  particular  ob- 
jects under  general  ideas,  and  show  their  conformity  to 
the  practice  and  manner  of  the  mathematicians  ;  it  re- 
mains only  to  observe,  that  the  true  way  of  rendering 
this  part  of  knowledge  both  easy  and  certain,  is,  by- 
habituating  ourselves  to  clear  and  determinate  ideas, 
and  keeping  them  steadily  annexed  to  their  respective 
names.  For  as  all  our  aim  is,  to  apply  general  words 
aright,  if  these  words  stand  for  invariable  ideas,  that 
are  perfectly  known  to  the  mind,  and  can  be  readily 
distinguished  upon  occasion,  there  will  be  little  danger 
of  mistake  or  error  in  our  reasonings.  Let  us  suppose, 
that  by  examining  any  object,  and  carrying  our  atten- 
tion successively  from  one  part  to  another,  we  have  "ac- 
quainted ourselves  with  the  several  particulars  observa-  . 
ble  in  it.  If  among  these  we  find  such  as  constitute 
some  general  idea,  framed  and  settled  beforehand  by 
the  understanding  and  distinguished  by  a  particular 
name^;  the  resemblance,  thus  known  and  perceived, 
necessarily  determines  the  species  of  the  object,  and 
thereby  gives  it  a  right  to  tie  jaame  by  whick  that  spc« 


142  DUNCAN'S  ELEMENTS 

ties  is  called.  Thus,  four  equal  sides,  joined  together 
at  right  angles,  make  up  the  notion  of  a  square.  As 
this  is  a  fixed  and  invariable  idea,  without  which  the 
general  name  cannot  be  applied,  we  never  call  any  par- 
ticular figure  a  square^  until  it  appears  to  have  these 
several  conditions  ;  and  contrarily,  wherever  a  figure 
is  found  with  these  conditions,  it  necessarily  takes  the 
name  of  a  square*  The  same  will  be  found  to  hold  in 
all  our  other  reasonings  of  this  kind;  where  nothing 
can  create  any  difficulty  but  the  want  of  settled  ideas. 
If,  for  instance,  we  have  not  determined  within  our- 
selves, the  precise  notion  denoted  by  the  word  man- 
slaughter*  it  will  be  impossible  for  us  to  decide,  whe- 
ther any  particular  action  ought  to  bear  that  name  : 
because,  however  nicely  we  examine  the  action  itself, 
yet  being  strangers  to  the  general  idea  with  which  it 
is  to  be  compared,  we  are  utterly  unable  to  judge  of 
their  agreement  or  disagreement.  But  if  we  take  care 
to  remove  this' obstacle,. and  distinctly  trace  the  two 
ideas  under  consideration,  all  difficulties  vanish,  and 
the  resolution  becomes  both  easy  and  certain. 

Sec.  VIII By  such   a    Conduct ;,    Certainty  and  De- 

moristration  might  be  introduced  into  other  Parts  of 
Knowledge  as  well  as  Mathematics* 

Thus  we  see  of  what  importance  it  is,  towards  the 
improvement  and  certainty  of  human  knowledge,  that 
we  accustom  ourselves  to  clear  and  determinate  ideas, 
and  a  steady  application  of  words.  Nor  is  this  so  easy  a 
task  as  some  may,  perhaps,  be  apt  to  imagine  ;  it  re- 
quiring both  a  comprehensive  understanding,  and  great 
command  of  attention,  to  settle  the  precise  bounds  of 
our  ideas,  when  they  grow  to  be  very  complex,  and 
include  a  multitude  of  particulars.  Nay,  and  after 
these  limits  are  duly  fixed,  there  is  a  certain  quickness 
of  thought  and  extent  of  mind  required,  towards  keep- 
ing the  several  parts  in  view,  that  in  comparing  our 
ideas  one  with  another,  none  of  them  may  -be  over- 
looked. Yet  ought  not  these  difficulties  to  discourage 
us  ;  though  great,  they  arc  not  un surmountable,  and 
tiic  advantages  arising  from  success  will  amply  recom- 


OF  LOGIC.  143 

pence  our  toil.  The  certainty  and  easy  application  of 
mathematical  knowledge  is  wholly  owing  to  the  exact 
observance  of  this  rule.  And  I  am  apt  to  imagine, 
that  if  we  were  to  employ  the  same  care4  about  all  our 
other  ideas,  as  mathematicians  have  done  about  those 
of.  number  and  magnitude,  by  forming  them  into  ex- 
act combinations,  and  distinguishing  these  combina- 
tions by  particular  names,  in  order  to  keep  them  steady 
and  invariable  ;  we  would  soon  have  it  in  our  power 
to  introduce  certainty  and  demonstration  into  other 
parts  of  human  knowledge. 


ctfmp,  in. 

OF  REASONING  AS  IT  REGARDS  THE  POWERS 
AND  PROPERTIES  OF  THINGS,  AND  THE  RE- 
LATIONS  OF  OUR  GENERAL  IDEAS. 

Sec.   I... .The  Distinction  of  Reasonings  as  it  regards 
tlie  Sciences,  and  as  it  concerns  common  Life. 

WE  come  now  to  the  second  great  end  which  men 
have  in  view  in  their  reasonings,  namely,  the 
discovering  and  ascribing  to  things  their,  several  attri- 
butes and  properties.  And  here  it  will  be  necessary  to 
distinguish  between  reasoning,  as  it  regards  the  sci- 
ences, and  as  it  concerns  common  life.  In  the  sciences, 
our  reason  is  employed  chiefly  about  universal  truths, 
it  being  by  them  alone  that  the  bounds  of  human 
knowledge  are  enlarged.  Hence  the  division  of  things 
into  various  classes,  called  otherwise  genera  and  spe- 
cies. For  these  universal  ideas,  being  set  up  as  the  re- 
presentatives of  many  particular  things,  whatever  is 
affirmed  of  them,  may  also  be  affirmed  of  all  the  indi- 
viduals to  which  they  belong.  Murder,  for  instance,  is 
a  general  idea,  representing  a  certain  species  of  human 
actions.  Reason  tells  us,  that  the  punishment  due  to  it 
is  death.  Hence  every  particular  action  coming  under 
the  notion  of  murder,  has  the  punishment  of  death  allot- 
ted to  it.  Here  then  we  apply  the  general  truth  to  some 
obvious  instance,  and  this  is  what  properly  constitutes 
•the  reasoning-  of  common  life.     For  men  in  their  ojrdi? 


14-4         DUNCAN'S  ELEMENTS 

nary  transactions  and  intercourse    one    with  another, 
have  for  the  most  part  to  do  only  with  particular  ob- 
jects.    Our  friends  and  relations,  their  characters  and 
behaviours,  the  constitution  of  the  several  bodies  that 
surround  us,  and  the  uses  to  which  they  may  be  appli- 
ed, are  what  chiefly  engage  our  attention.   In  all  these 
we  reason  about  particular  things  j    and  the  whole  re- 
sult of  our  reasoning  is,  the  applying  the  general  truths 
of  the  sciences  to  the  ordinary  transactions  of  human 
life.     When  we  see  a  viper,  we  avoid    it.    Wherever 
we  have  occasion  for  the  forcible  action  of  water,   to 
move   a  body  that  makes  considerable  resistance,  we 
take    cave  to  convey  it  in  such  a  manner,  that  it  shall 
fall  upon  the  object  with  impetuosity.      Now  all  this 
happens,  in   consequence  of  our  familiar  and  ready  ap- 
plication of  these  two  general  truths  :  the  bite  of  a  vi- 
per is  mortal :  water  falling  on  a  body  with  impetuosi- 
ty,  acts  very  forcibly  towards  setting  it  in  motion.      In 
like  manner,  if  we  set  ourselves  to  consider  any  parti- 
cular character,  in    order  to    determine    the  share    of 
praise  or  dispraise  that    belongs  to    it,  our  great  con- 
cern is,    to  ascertain  exactly  the  proportion  of  virtue 
•  and  vice.     The  reason  is  obvious.     A  just  determina- 
tion, in  all  cases  of  this  kind,    depends   entirely  upon 
•  an  application  of  these  maxims  of  morality:    virtuous 
.actions  deserve  praise  ;    vicious  actions  deserve  blame. 

Sec.  II....  The  Steps  by  which  we  proceed  in  the  Reason- 
ing of  common  Life. 

Hence  it  appears,  that  reasoning,  as  it  regards  com- 
mon life,  is  no  more  than  the  ascribing  the  general  pro- 
perties of  things  to  those  several  objects  with  which 
we  are  immediately  concerned,  according  as  they  are 
found  to  be  ot  that  particular  division  or  class  tor 
which  the  properties  belong.  The  steps,  then,  by  which 
we  proceed,  are  manifestly  these.  First,  we  refer  the 
object  under  consideration  to  some  general  idea  or 
class  of  things.  We  then  recollect  the  several  attri- 
butes of  that  general  idea  ;  and,  lastly,  ascribe  all 
those  attributes  to  the  present  object.  Thus  in  consi- 
dering the  character  of  Sempronius}  if  we  find  it  to  be 


OF  LOGIC.  145 

of  the  kind  called  virtuous  ;  when  we  at  the  same  time 
reflect,  that  a  virtuous  character  is  deserving  of  esteem, 
it  naturally  and  obviously  follows,  that  Sempronius  is 
so  too.  These  thoughts  put  into  a  Syllogism^  in  or- 
der to  exhibit  the  form  of  reasoning  here  required  runs 
thus  : 

Every  virtuous  man  is  worthy  of  esteem., 
Sempronius  is  a  virtuous  man  : 
Therefore  Sempronius  is  worthy  of  esteem. 

Sec.  III....  The   Connexion  and  Dependence  of  the  tivt- 
grand  Branches  of  Reasoning  one  upon  another. 
By  this* syllogism  it  appears,  that  before  we  affirm 
any  thing  of  a  particular  object,   that  object  must  be 
referred  to  some  general  idea.  Sempronius  is  pronounced 
worthy  of  esteem,  only  in  consequence  of  his  being  a 
virtuous   man,   or  coming  under  that   general  notion. 
Hence  we  see  the  necessary  connexion  of  the  various 
parts  of  reasoning,  and  the  dependence  they  have  one  . 
upon  another.     The  determining  the  genera  and  spe- 
cies of  things  is,  as  we  have  said,  one  exercise  of  hu- 
man reason  ;  and  here  we  find  that  this  exercise  is  the 
first   in  order,  and  previous  to  the  other,   which  con- 
sists in  ascribing  to  them  their  powers,  properties,  ancl 
relations.  But  when  we  have  taken  this  previous  step,' 
and  brought   particular  objects  under  general  names  ; 
as  the  properties  we  ascribe  to  them  are  no  other  than- 
those  of  the  general  idea,  it  is -plain,  that  in  order  to  a 
successful  progress  in  this  part  of  knowledge,  we  must 
thoroughly  acquaint    ourselves  with  the   several  rela- 
tions and  attributes  of  these  our  general  ideas.  When 
this  is  done,  the  other  part   will  be  easy,  and  require 
scarce   any  labour  of  thought,   as  being  no  more  than 
an  application  of  the  general  form  of  reasoning  repre- 
sented in  the  foregoing  syllogism.     Now,   as  we  have 
already   sufficiently  shown,  how  we  are  to  proceed  in 
determining  the  genera  and  species  of  things,  which 
as  we    have  said,    is  the   previous  step  to  this  second 
branch  of  human  knowledge  ;  all  that  is  farther  want- 
ing to  a  due  explanation  of  it  is,  to  offer  some  consi-  , 
derations,  as  to  the  manner  of   investigating  the    ge- 
neral relations  of  our  ideas.     This  is  the  highest  exer* 
N 


146  DUNCAN'S  ELEMENTS 

cise  of  the  powers  of  the  understanding,  and  that  by- 
means  whereof,  we  arrive  at  the  discovery  of  univer- 
sal truths  ;  insomuch  that  our  deductions  in  this  way, 
constitute  that  particular  species  of  reasoning,  which, 
we  have  before  said,  regards  principally  the  sciences. 

Sec.  IV....TW0  things  required  to  make  a  good  Rea- 
sorter. 
But  that  we  may  conduct  our  thoughts  with  some 
order  and  method,  we  shall  begin  with  observing,  that 
the  relations  of  our  general  ideas  are  of  two  kinds. 
Either  such  as  immediately  discover  themselves,  upon 
comparing  the  ideas  one  with  another;  or  such,  as  be- 
ing more  remote  and  distant,  require  art  and  contriv- 
ance to  bring  them  into  view.  The  relations  of  the 
€rst  kind,  furnish  us  with  intuitive  and  self-evident 
truths  :  those  of  the  second  are  traced  by  reasoning, 
and  a  due  application  of  intermediate  ideas.  It  is  of 
this  last  kind  that  we  are  to  speak  here,  having  dis- 
patched what  was  necessary  with  regard  to  the  other 
in  the  second  part.  As  therefore  in  tracing  the  more 
distant  relations  of  things,  we  must  always  have  re- 
course to  intervening  ideas,  and  are  more  or  less  suc- 
cessful in  ourrescarches,  according  to  our  acquaintance 
with  these  ideas,  and  ability  of  applying  them  ;  it  is 
evident,  that  to  make  a  good  reasoner,  two  things  are 
principally  required.  First,  an  extensive  knowledge 
of  those  intermediate  ideas  by  means  of  which  things 
may  be  compared  one  with  another.  Secondly,  the  skill 
and  talent  of  applying  them  happily,  in  all  particular 
instances  that  come  under  consideration. 

Sec.  V... .First,  an  extensive  Knowledge  of  intermedi- 
ate Ideas. 
*  Eirst,  I  say,  that  in  order  to  our  successful  progress 
in  reasoning,  we  must  have  an  extensive  knowledge  of 
those  intermediate  ideas  by  means  of  which  things  may 
be  compared  one  with  another.  For  as  it  is  not  every 
idea  that  will  answer  the  purpose  of  our  enquiries,  but 
such  only  as  are  peculiarly  related  to  the  objects  aboi.it 
which  we  reason,  so  as  by  a  comparison  with  them,  to 
fornish  evident  and  known  truths  t  nothing  is  mbit 


OF  LOGIC.  24* 

apparent,  than  that  the  greater  variety  of  conception* 
we  can  call  into  view,  the  more  likely  we  are  to  find 
some  among  them  that  will  help  us  t6  the  truths  here 
required.  And  indeed  it  is  found  to  hold  in  experiene, 
that  in  proportion  as  we  enlarge  our  view  of  things, 
and  grow  acquainted  with  a  multitude  of  different  ob» 
jects,  the  reasoning  quality  gathers  strength.  For  by 
extending  our  sphere  of  knowledge,  the  mind  acquires 
a  certain  force  and  penetration,  as  being  accustomed 
to  examine  the  several  appearances  of  its  ideas,  and 
observe  what  light  they  cast  one  upon  another. 

Sec.  VI....  To  excell  in  any  one  Branch  of  Learning, 
we  must  in  general  be  acquainted  with  the  whole  cir- 
cle of  Arts  and  Sciences. 

And  this  I  take  to  be  the  reason,  that  in  order  to 
excel  remarkably  in  any  one  branch  of  learning,  it  is 
necessary  to  have  at  least  a  general  acquaintance  with 
the  whole  circle  of  arts  and  sciences."  The  truth 
of  it  is,  all  the  various  divisions  of  human  knowledge 
are  very  nearly  related  among  themselves,  and -innu- 
merable instances  serve  to  illustrate  and  set  off  each  « 
other.  And  although  it  is  not  to  be  denied,  tha^:  by 
an  obstinate  application  to  one  branch  of  study,  a  man 
may  make 'considerable  progress,  and  acquire  some  de- 
gree.ot:  eminence  in  it  ;  yet  his  views  will  be  always 
narrow  and  contracted,  and  he  will  want  that  master- 
ly discernment  which  not  only  enables  us  to  pursue 
our  discoveries  with  ease,  but  also  in  laying  them  open 
to  others,  to  spread  a  certain  brightness  around  them. 
I  would  not,  however,  here  be  understood  to  mean, 
that  a  general  knowledge  alone  is  sufficient  for  all  the 
purposes  of  reasoning.  I  only  recommend  it  as  .pro- 
per to  give  the  mind  a  certain  sagacity  and  quickness, 
and  qualify  it  for  judging  aright  in  the  ordinary  oc-»  - 
currences  of  life.  But  when  our  reasoning  regards  a 
particular  science,  it  is  farther  necessary,  that  we  more 
nearly  acquaint  ourselves  with  whatever  relates  to  that 
science.  A  general  knowledge  is  a  good  preparation, 
and  enables  us  to  proceed  with  ease  and  expedition  in 
whatever  branch  of  learning  we  apply  to.     But  then 


US  DUNCAN'S  ELEMENTS 

in  the  minute  and  intricate  questions  of  any  science* 
-we  are  by  no  means  qualified  to  reason  with  advantage, 
until  we  have  perfectly  mastered  the  science  to  which 
they  belong  ;  it  being  hence  chiefly  that  we  are  fur- 
nished with  those  intermediate  ideas,  which  lead  to  a 
just  and  successful  solution.       „ 

Sec.  VII...  .Why  Mathematicians  sometimes  answer  not 
the  expectation  their  great  learning  raises. 

And  here,  as  it  comes  so  naturally  in  my  way,  I  can* 
not  avoid  taking  notice  of  an  observation  that  is  fre- 
quently to  be  met  with,  and  seems  to  carry  in  it  at 
first  sight  something  very  strange  and  unaccountable. 
It  is,  in  short,  this,  that  mathematicians,  even  such  at* 
are  allowed  to  excel  in  their  own  profession,  and  to 
have  discovered  themselves  perfect  masters  in  the  art 
of  reasoning,  have  not  yet  been  always  happy  in  treat- 
ing upon  other  subjects  ;  but  rather  fallen  short,  not 
only  what  might  naturally  have  been  expected  from 
them,  but  of  many  writers  much  less  exercised  in  the 
rules  of  the  argumentation.  This  will  not  appear  so 
very  extraordinary,  if  we  reflect  on  what  has  been 
hinted'  above.  Mathematics  is  an  engagittg  study  :  and 
inert  who  apply  themselves  that  way,  so  wholly  plunge 
into  it,  that  they  are  for  the  most  part  but  little  ac- 
quainted with  other  branches  of  knowledge.  Whenr 
'therefore,  they  quit  their  favorite  subject,  and  enter 
.upon  others,  that  are  in  a  manner  new  and  strange  to 
them,  no  wonder  if  they  find  their  invention  at  a 
stand.  Because,  however  perfect  they  may  be  iruthe 
art  of  reasoning,  yet  wanting  here  those  intermediate 
ideas  whieh  are  necessary  to  furnish  out  a  due  train  of 
propositions,  all  their  skill  and  ability  fails  them.  For 
a  bare  knowledge  of  the  rules  is  not  sufficient. •  We 
must  farther  have  materials'whereunto  to  apply  them. 
And  when  these  are  once  obtained,  then  it  is  that  an  able 
reasoner  discovers  his  superiority,  by  the  just  choice  he 
makes,  and  a  certain  masterly  disposition,  that-in  eve- 
ry step  of  the  procedure  carries  evidence  and  convic- 
tion along  with  it.  Andhence  it  is,  that  such  mathe- 
maticians as  have  of  late  years  applied  themselves  to 


OF  LOGIC.  U9 

oilier  sciences,  'and  not  contented  with  a  superficial 
knowledge,  endeavoured  to  reach  their  inmost  re- 
cesses ;  such  mathematicians,  I  say,  have  by  mere 
strength  of  mind,  and  a  happy  application  of  geome- 
trical reasoning,  carried  their  discoveries  far  beyond 
-what  was  heretofore  judged  the  utmost  limits  of  hu- 
man knowledge.  This  is  a  truth  abundantly  known  to 
all  who  are  acquainted  with  the  late  wonderful  im- 
provements in  natural  philosophy. 

Sec.   V III. ..Secondly ,  the  Skill  of  applying  Intermedi- 
ate Ideas  happily  in  particular  instances, 

I  come  now*  to  the  second  thing  required, in  order 
to  a  successful  progress  in  reasoning,  namely  ;  the  skill 
and  talent  of  applying  intermediate   ideas   happily  in 
all  particular  instances  that  come  under  consideration. 
And  here  I  shall  nottake  up  much  time  in  laying  down  . 
rules   and  precepts,   because   I  am  apt  to   think  they 
would  do  but  little  service.     Use  and  exercise  are  th^ 
best  instructors  in  the  present  case  :   and  whatever  lo- 
gicians  may  boast,  of  being  able  to  form  perfect  rea- 
soners   by  book  and  rule,  yet  we  find  by  experience, 
that   the  study  of  their  precepts  does  not  always  add 
any  great  degree  of  strength  to  the  understanding.  In 
short,  'tis  the  habit  alone  of  reasoning  that  makes  a 
reasoner.     And  therefore  the  true  way  to  acquire  this 
talent,  is,  by  being  much  conversant  in  those  sciences 
where  the  art  of  reasoning  is  allowed  to  reign  in  the 
greatest  perfection.     Hence  it  was,  that  the  ancients, 
who  so  well  understood  the  manner   of  forming  the 
mind,  always  began  with  mathematics  as  the  founda- 
tion of  their  philosophical  studies.     Here  the  under- 
standing is  by  degrees  habituated  to  truth,  contracts, 
insensibly  a  certain  fosdness  for  it,  and   learns  never 
to  yield  its  assent  to  any  proposition,  but  where  the.# 
evidence  is  sufficient  to  produce  full  conviction.     For 
this  reason  Plato  has  called  mathematical  demonstra-' 
tions  the  cathartics  or  purgatives  of  the  soul,  as  be- 
ing the  proper  means  to  cleanse  it  from  error,  and  re- 
store that   natural  exercise  of  its  faculties   in    which 
•just  thinking  consists.     And  indeed  I  beJieve  it  will 
N  2 


150  DUNCAN'S  ELEMENTS 

be  readily  allowed,  that  no  science  furnishes  so  many 
instances  of  a  happy  choice  of  intermediate  ideas,  and 
a  dexterous  application  of  them,  for  the  discovery  of 
truth  and  enlargement  of  knowledge. 

.Sec.  IX*"**  The  Study  of  Mathematical  Demonstrations 
.  of  great  avail  in  this  respect. 

If,  therefore,  we  would  form  our  minds  to  a  habit  of 
reasoning  closely  and  in  train,  we  cannot  take  any- 
more certain  method,  than  the  exercising  ourselves  in 
mathematical  demonstrations,  so  as  to  contract  a  kind 
of  familiarity  with  them,  "  not  that  we  look  upon  it 
as  necessary,  (To  use  the  words  of  the  great  Mr. 
LockeJ  that  all  men  should  be  deep  mathematicians, 
but  that,  having  got  the  way  of  reasoning  which  that 
study  necessarily  brings  the  mind  to,  they  may  be 
able  to  transfer  it  to  other  parts  of  knowledge,  as  they 
shall  have  occasion.  For  in  all  sorts  of  reasoning  every 
single. argument  should  be  managed  as  a  mathematical 
demonstration,  the  connexion  and  dependence  of  ideas 
should  be  followed,  till  the  mind  is  brought  to  -  the 
source  on  which  it  bottoms,  and  can  trace  the  cohe- 
rence through  the  whole  train  cf  proofs.  It  is  in  the 
general  observable,  that  the  faculties  of  our  souls  are 
improved  and  m?.de  useful  to  us  just  after  the  same 
manner  as  our  bodies  are.  Would  yeu  have  a  man 
write  or  paint,  dance  or  fence  well,  or  perform  any 
other  manual  operation,  dexterously  and  with  ease  ? 
Let  him  have  ever  so  much  vigour  and  activity,  sup- 
pleness and  address  naturally,  yet  no  body  expects 
this  from  him,  unless  he  has  been  used  to  it,  and  has 
employed  time  and  pains  in  fashioning  and  forming 
his  hand,  or  outward  parts  to  these  motions.  Just  so 
It  is  in  the  mind  ;  would  you  have  a  man  reason  well, 
.you  must  use.  him  to  it  betimes,  exercise  his  mind  in 
observing  the  connexion  of  ideas,  and  following  them 
in  train.  Nothing  does  this 'better  than  mathematics  ; 
which,  therefore,  I  think  should  be  taught  all  those 
who  have  the  time  and  opportunity,  not  so  much  to 
make  them  mathematicians,  as  to  make  them  reasona- 
ble creatures  5  for  though  we  all  call  ourselves  so,  be- 


OF  LOGIC.  151 

i 

cause  we  are  born  to  it,  if  we  please  ;  yet  we  may 
truly  say,  nature  gives  us  but  the  seeds  cf  it.  We  are 
born  to  be,  if  we  please,  rational  creatures  ;  but  'tis 
use  and  exercise  only  that  makes  us  sb,  and  we  are  in- 
deed so,  no  farther  than  industry  and  application  has 
carried  us. "     Conduct  of  the  Understanding, 

Sec.  X As  also  of  such  Authors  on  other  Subjects,  a$ 

are  distinguished  for  Strength  and  Justness  of  Re  a* 
soning. 

But  although  the  study  of  mathematics  be,  of  all 
others,  the  most  useful  to  form  the  mind  and  give  it 
an  early  relish  of  truth,  yet  ought  not  other  parts  of 
philosophy  to  be  neglected.  For  there  also  we  meet 
with  many  opportunities  of  exercising  the  powers  of 
the  understanding  ;  and  the  variety  of  subjects  natu- 
rally lead  us  to  observe  all  those  different  turns  of 
thinking  that  are  peculiarly  adapted  to  the  several 
ideas  we  examine,  and  the  truths  we  search  after.* 
A  mind  thus  trained,  acquires  a  certain  mastery  over 
its  own  thoughts,  insomuch  that  it  can  range  and  mo- 
del them  at  pleasure,  and  call  such  into  view  as  best 
suit  its  present  designs.  Now  in  this  the  whole  art  of 
reasoning  consists,  from  among  a  great  variety  of  dif- 
ferent ideas,  to  single  out  those  that  are  most  proper 
for  the  business  in  hand,  and  to  lay  them  together  in  * 
such  order,  that  from  plaia  and  easy  beginnings,  by 
gentle  degrees,  and  a  continual  train  of  evident  truths, 
we  may  be  insensibly  led  on  to  such  discoveries,  as  at 
our  first  setting  out,  appeared  beyond  the  reach  of  the 
human  understanding.  For  this  purpose,  besides  the 
study  of  mathematics  before  recommended,  we  ought 
to  apply  ourselves  diligently  to  the  reading  of  such 
authors  as  have  distinguished  themselves  for  strength 
of  reasoning,  and  a  just  and  accurate  manner  of  think- 
ing. For  it  is  observable,  that  a  mind  exercised  and' 
seasoned  to  truth  seldom  rests  satisfied  in  a  bare  eon- 
templation  of  the  arguments  offered  by  others, .  but 
^will  be  frequently  essaying  its  own  srength,  and  pur- 
suingits  discoveries  upon  the  plan  it  is  most  accustom- 
ed to.     Thus  wc  insensibly  contract  a  Jiabit  of  tracing 


152  DUNCAN'S  ELEMENTS 

truth  from  one  stage  to  another,  and  of  investigating 
those  general  relations  and  properties  which  we  af- 
terwards ascribe  to  particular  things,  according  as  we 
find  them  comprehended  under  the  abstract  ideas  to 
which  the  properties  belong.  And  thus  having  parti- 
cularly shown  how  we  are  to  distribute  the  several  ob- 
jects of  nature  under  general  ideas,  what  properties 
jwe  are  to  ascribe  to  them  in  consequence  of  that  distri- 
bution*, and  how  to  trace  and  investigate  the  properties 
themselves  ;  I  think  I  have  sufficiently  explained  all 
that  is  necessary  towards  a  due  conception  of  reason- 
ing, and  shall  therefore  here  conclude  this  chapter. 


OF  THE  FORMS  OF  SYLLOGISMS. 

Sec,  I....TAe  Figures  of  Syllogisms* 

HITHERTO  we  have  contented  ourselves  with  a 
general  notion  of  syllogisms,  and  of  the  parts  of 
which  they  consist.  It  is  now  time  to  enter  a  little 
more  particularly  into  the   subject,   to  examine  their 

•  various  forms,  and  to  lay  open  the  rules  of  argumen- 
'  tation  proper  to  each.     In  the  syllogisms  mentioned  in 

the  foregoing  chapters,  we  may  observe,  that  the  middle 
\erm  is  the  subject  of  the  major  proposition,  and  the 
^predicate  of  the  minor*.  This  disposition,  though  the 
m6st  natural  and  obvious,  is  not,  however,  necessary  ; 
it  frequently  happening,  that  the  middle  term  is  the 
subject  in  both  the  premises,  or  the  predicate  in  both  ; 
and  sometimes,  directly  contrary  to  its  disposition  in 
the  foregoing  chapters,  the  predicate  in  the  major ,  and 
the  subject  in  the  minoie*  Hence  the  distinction  of  syl- 
logisms into  various  "CTnds,  called  figures  by  logician's. 
•    Toy  figure,  according  to  their  use  of  the  word,  is*  no- 

•  thing  else  but  the  order  and  disposition  of  the  middle 
term  In  any  syllogism.  And  as  this  disposition  is,"  we 
see.  four-fold,  so  the  figures  of  syllogisms  thence  aria- 


OF  LOGIC.  1535 

ing  are  four  in  number*  When  the  middle  term  is  the 
subject  of  the  major  proposition,  and  the  predicate  of 
the  minor,  we  have  what  is  called  fhe  Jirst  figure.  If 
on  the  other  hand,  it  is  the  predicate  of  both  the  pre- 
mises, the  syllogism  is  said  to  be  in  the  second  figure* 
Again,  in  the  third  figure,  the  midddle  term  is  the  sub-. 
ject  of  the  two  premises.  And  lastly,  by-making  it  the 
predicate  of  the  major,  and  subject  of  the  .minor,  we 
obtain  syllogisms  in  the  fourth  figure. 

Sec.  II...  .The  Moods  of  Syllogisms. 
But  besides  this  fourfold  distinction  of  syllogisms, 
there  is  also  a  farther  subdivision  of > them  in  every  fi- 
gure, arising  from  the  quantity  and  quqlity,zs  they  are 
called,  of  the  propositions*  By  quantity  we  mean  the 
consideration  of  propositions  as  universal  or  particular, 
by  quality  as  affirmative  or  negative.  Now  as  in  all  the 
scveraldispositionsof  the  middle  term,  the  propositions, 
of  which  a  syllogiim  consists,  may  be  either  universal 
or  particular,  affirmative  or  negative  ;  the  due  determi- 
nation of  these,  and  so  putting  them  together  as  the 
laws  of  argumentation  require,  constitute  what  logici- 
ans call  the  moods  of  syllogisms.  Of  these  moods  there 
are  a  determinate  number  to  every  figure,  "including 
all  the  possible  ways  in  which  propositions  differing  in 
quantity  or  quality  can  be  combined,  according  to  any 
disposition  of  the  middle  term,  in  order  to  arrive  at  a 
just  conclusion.  The  shortness  of  the  present  work 
will  not  allow  of  enteringjnto  a  more  particular  des- 
cription of  these  several  distinctions  and  divisions.  I 
shall  therefore  content  myself  with  referring  the  rea- 
der to  the: Port  Royal  art  of  thinking,  where  he  will 
find  the  moods  and  figures  of  syllogisms  distinctly  ex- 
plained, and  the  rules  proper  to  each  very  neatly  de- 
monstrated. 

Sec.  III.... Foundation  of  the  other 'Divisions  of  Syl- 
logisms.. .  '. 
The  division  of  syllogisms  according  to  mocd  and 
figure,  respects  those  especially,  which  are  known  by 
the  name  of  plain  simple  syllogisms ;  that  is,  which  are 
bounded  to  three  propositions,  all  simple,  and  where. 


154  DUNCAN'S  ELEMENTS 

the  extremes  and  middle  term  are  connected,  accord- 
ing to  the  rules  laid  down  above.  But  as  the  mind  is 
not  tied  down  to  any  one  precise  form  of  reasoning, 
but  sometimes  makes  use  of  more,  sometimes  of  few- 
er premises,  and  often  takes  in  compound  and  conditi- 
onal propositions,  it  may  not  be  amiss  to  take  notice 
"cf  the  different  forms  derived  from  this  source,  and  ex- 
plain the  rules  by  which  the  mind  conducts  itself  in 
the  use  of  them. 

Sec.  IV....  Conditional  syllogisms. 
When  in  any  syllogism,   the  major  is  a  conditional 
proposition,  the   syllogism  itself  is  termed  conditional 
Thus  : 
If  there  is  a  God,  he  ought  to  be  worshipped. 
But  there  is  a  God: 

Therefore  he  ought  to  be  worshipped, 
In  this  example,  the  major  or  first  proposition,  is  we 
see,  conditional,  and  therefore  the  syllogism  itself  is 
also  of  the  kind  called  by  that  name.  And  here  we 
are  to  observe,  that  all  conditional  propositions  are 
made  up  of  two  distinct  parts  ;  one  expressing  the 
condition  upon  which  the  predicate  agrees  or  disagrees 
with  trie  subject,  as  in  this  now  before  us,  if  there  is  a 
God;  the  other  joining  or  disjoining  the  said  predi- 
cate aild  subject,  as  here,  he  ought  to  be  worshipped.  The 
first  of  these  parts,  or  that  which  implies  the  condi- 
tion, is  called  the  antecedent ;  the  second,  where  we 
join  or  disjoin  the  predicate  and  subject,  has  the  name 
of  the  consequent. 

Sec.  V.,»*Grou?id  of  Illation  in  conditional  Syllogisms, 
.  These  things  explained,  we  are  farther  to  observe, 
that  in  all  propositions  of  this  kind,  supposing  thera 
to  be  exact  in  point  of  form,  the  relation  between  the 
antecedent  and  consequent,  must  ever  he  true  and 
real ;  that  is,  the  antecedent  must  always  contain 
some  certain  and  genuine  condition  which  necessa- 
rily implies  the  .consequent;  for  otherwise,  the  pro- 
position itself  will  be  false,  and  therefore  ought  not 
to  be  admitted  into  our  reasoning?.  Hence  it  follows, 
that  when  any  conditional  proposition  is  assumed,  if 
we  admit  the  antecedent  of  that  proposition,  we  must, 


OF  LOGIC.  15* 

at  the  same  time,  necessarily  admit  the  consequent : 
but  if  we  reject  the  consequent,  we  are,  in  like  man« 
ner,  bound  to  reject  also  the  antecedent.  For  as  the 
antecedent  always  expresses  some  condition  which. ne- 
cessarily implies  the  truth  of  the  consequent;  by  ad- 
mitting the  antecedent,  we  allow  of  that  condition, 
and  therefore  ought  also  to  admit  the  consequent.  In 
like  manner,  if  it  appears  that  the  consequent  ought 
to  be  rejected,  the  antecedent  evidently  must  be  so 
too  ;  because,  as  we  just  now  demonstrated,  the  ad- 
mitting of  the  antecedent  would  necessarily  imply  the 
admission  also  of  the  consequent. 

Sec.  Vl.„,The  two  Moods  of  Conditional  Syllogism. 

From  what  has  been  said,  it  appears,  that  there  are 
two  ways  of  arguing  in  hypothetical  syllogism,  which 
lead  to  a  certain  and  unavoidable  conclusion.  For  as  the 
major  is  always  a  conditional  proposition,  consisting  of 
an  antecedent  and  a  consequent ;  if  the  minor  admits 
the  antecedent,  it  is  plain,  that  the  conclusion  must  ad- 
mit the  consequent.  This  is  called  arguing  from  the 
admission  ofthe  antecedent  to  the  admission  of  the  con- 
sequent, and  constitutes  that  mood  or  species. of  hypo* 
tlietical  syllogisms,  which  is  distinguished  in  the  schools 
by  the  name  of  the  modus ponens,  inasmuch  as  by  it  the 
whole  conditional  proposition,  both  antecedent  and 
consequent,  is  established.     Thus, 

If  God  is  infinitely  wise,  and  acts  with  perfect  freedom^he 

does  nothing  but  what  is  best 
But  God  is  infinitely  wise,  and  acts  with  perfect  freedom, 
Therefore  he  does  nothing  but  what  is  best. 

Here  we  see  the  antecedent  or  first  part  ofthe  con- 
ditional proposition  is  established  in  the  minor,  and  the 
consequent  or  second  part  in  the  conclusion  ;  whence 
the  syllogism  itself  is  an  example  of  the  modus  penens* 
But  if  now  we  on  the  contrary  suppose,  that  the  minor 
rejects  the  consequent,  then  it  is  apparent,  that  the 
conclusion  must  also  reject  the. antecedent.  In  this  case 
we  are  said  to  argue  from  the  removal  ofthe  consequent, 
to  the,  removal  of  the  antecedent ;  and  the  particular 
mood  or  species  of  syllogism  thence  arising  is  called  bjr 


156         DUNCAN'S  ELEMENTS 

logiciansthe  modus  tollehs  ;  because  in  it,  both  antece- 
dent and  consequent  are  rejected  or  taken  away,  as  ap- 
pears by  the  following  example  : 

If  God  were  not  a  being  of  infinite  goodness,  neither  would 
he  consult  the  happiness  of  his  creatures. 
But  God  does  consult  the  happiness  of  his  creatures : 
Therefore  He  is  a  Being  of  Infinite  Goodness. 

Sec,  VIL...  T/zey  include  all  the  Legitimate  Ways  of 
Arguing. 
These  two  species  take  in  the  whole  class  of  conditi- 
onal syllogisms,  and  include  all  the  possible  ways  of 
arguing  that  lead  to  a  legitimate  conclusion  ;  because 
we  cannot  here  proceed  by  a  contrary  process  of  rea- 
soning, that  is,  from  the  removal  of  the  antecedent  to 
the  removal  of  the  consequent,  or  from  the  establish- 
ing of  the  consequent  to  the  establishing  of  the  ante- 
cedent. For  although  the  antecedent  always  expresses 
some  real  condition,  which,  once  admitted,  necessarily 
implies  the  consequent,  yet  it  does  not  follow,  that 
there  is  therefore  no  other  condition  ;  and  if  so,  then, 
after  remoring  the  antecedent,  the  consequent  may 
still  hold,  because  of  some  other  determination  that  in- 
fers it."  When  we  say:  If  a  stone  is  exposed  some 
time  to  the  rays  of  the  sun,  it  will  contract  a  certain 
degree  of  heat  ;  the  proposition  is  certainly  true,  and, 
admitting  the  antecedent,  we  must  also  admit  the  con- 
sequent. But  as  there  are  other  ways  by  which  a  stone 
may  gather  heat,  it  will  not  follow  from  the  ceasing 
of  the  before -mentioned  condition,  that  therefore  the 
consequent  cannot  take  place.  In  other  words,  we 
cannot  argue,  but  the  stone  has  not  been  exposed  to  the 
rqys  of  the  suy, ;  therefore  neither  has  it  any  degree  of 
heat ;  inasmuch  as  there  are  a  great  many  other  ways 
by  which  heat  might  have  been  communicated  to  it. 
And  if  we  cannot  argue  from  the  removal  of  the  antece- 
dent to  the  removal  of  the  consequent,  no  more  can  we 
from  the  admission  of  the  consequent  to  the  admis- 
.  sion  of  the  antecedent.  Because  as  the  consequent 
may  flow  from  a  great  variety  of  different  suppositi- 
ons, the  allowing  of  it  does  not  determine  the  precise 
■aupposition,    but  only  that   some  of  them  must  take 


OF  LOGIC.  15t 

place.  Thus  in  the  foregoing  reposition,  if  a  stone 
is  exposed  some  time  to  the  rays  of  the  sun,  it  will  con- 
tract a  certain  degree  of  beat  :  admitting  the  conse- 
quent, viz.  that  it  has  contracted  a  certain  degree  of 
heat)  we  are  not  therefore  bound  to  admit  the  ante- 
cedent, that  it  has  been  some  time  exposed  to  the  rays  of 
the  sun  ;  because  there  are  many  other  causes  whence 
that  heat  may  have  proceeded.  These  two  ways  of 
arguing,  therefore,  hold  not  in  conditional  syllogisms. 
Indeed,  where  the  antecedent  expresses  the  only  condi- 
tion on  which  the  consequent  takes  place,  there  they  " 
maybe  applied  with  safety  ;  because,  wherever  that  con- 
dition is  not,  we  are  sure  that  neither  can  the  consequent 
be,  and  so  may  argue  from  the  removal  of  the  one  to  * 
the  removal  of  the  other  ;  as,  on  the  contrary,  where- 
ver the  consequent  holds,  it  is  certain  that  the  condition 
must  also  take  place  ;  which  shows,  that  by  establish- 
ing the  consequent,  we  at  the  same  time  establish  the 
antecedent.  But  as  it  is  a  very  particular  case,  and 
that  happens  but  seldom,  it  cannot  be  extended  into  a 
general  rule,  and  therefore  affords  not  any  steady  and 
universal  ground  of  reasoning  upon  the  two  foregoing 
suppositions. 

Sec.  Villi...  The  Manner  of  Arguing  in  Disjunctive 
Syllogisms, 

As  from  the  majors  being  a  conditional  proposition, 
we  obtain  the  species  of  conditional  syllogisms  ;  so 
where  it  is  a  disjunctive  proposition,  the  syllogism,  to 
which  it  belongs,  is  called  disjunctive,  as  in  the  follow- 
ing example  : 

The  world  is  cither  self-existent,  or  the  work  of  some-  fi-' 
nite  or  of  some  infinite  being. 

But  it  is  not  self-existent,  nor  the  work  of  a  finite  being  : 

Therefore  it  is  the  work  of  an  infinite  being. 

Now  a  disjunctive  proposition  is  thatwbere  of  seve* 
ral  predicates  we  afnrm  one  necessarily  to  belong  to 
the  subject,  to  the  exclusion  of  all  the  rest,  but  leave 
that  particular  one  undetermined.  Hence  it  follows, 
that  as  soon  as  we  determine  the  particular  predicate, 
all  the  rest  are  of  course  to  be  rejected  ;  or  if  we  re- 
ject all  the  predicates  but  one,  that  one  necessarily 
O 


158  DUNCAN'S  ELEMENTS 

takes  place.  When,  therefore,  in  a  disjunctive  syllo- 
gism, the  several  predicates  are  enumerated  in  the  #jcr- 
jor....\f  the  minor  establishes  any  one  of  these  predi- 
cates, the  conclusion  ought  to  remove  all  the  rest ;  or 
if,  in  the  minor,  all  the  predicates  but  one  are  remov- 
ed, the  conclusion  must  necessarily  establish  that  one* 
Thus  in  the  disjunctive  syllogism  given  above,  the  ma- 
jor affirms  one  of  three  predicates  to  belong  to  the 
earth,  viz.  self -existence,  or  that  it  istlie  work  of  a  finite, 
or  that  it  is  the  work  of  an  infinite  being.  Two  of  these 
predicates  are  removed  in  the  minor,  viz.  self-existence, 
and  the  work  of  a  finite  being.  Hence  the  conclusion 
necessarily  ascribes  to  it  the  third  predicate,  and  af- 
firms, that  it  is  the  work  of  an  infinite  being.  If  now 
we  give  the  syllogism  another  turn,  insomuch  that  the 
minor  may  establish  one  of  the  predicates,  by  affirming 
the  earth  to  be  the  production  of  an  infinite  being.... 
then  the  conclusion  must  remove  the  other  two,  assert- 
ing it  to  be  neither  self-existent,  nor  the  work  of  a  fi- 
nite being.  These  are  the  forms  of  reasoning  in  this 
•species  of  syllogisms,  the  justness  of  which  appears  at 
first  sight ;  and  that  there  can  be  no  other,  is  evident 
frpni  the  very  nature  of  adisjunctive  proposition. 

Sec. ...IX.  Imperfect  or  mutilated  Syllogisms. 
In  the  several  kinds  of  syllogisms  hitherto  mention- 
ed, we  may  observe,  that  the  parts  are  complete  ;  that 
is,  the  three  propositions  of  which  they  consist  are  re- 
presented in  form.  But  it  often  happens,  that  some 
one  of  the  premises  is  not  only  an  evident  truth,  but 
also  familiar  and  in  the  minds  of  all  men  ;  in  which 
case  it  is  usually  omitted,  whereby  we  have  an  imper- 
fect syllogism,  that  seems  to  be  made  up  of  only  two 
proposition.  Should  we,  for  instance,  argue  in  this 
manner : 

Every  man  is  mortal ; 

Therefore  every  king  is  mortal  ; 
the  syllogism  appears  to  be  imperfect,  as  consisting  byt 
of  two  propositions.  Yet  it  is  really  complete,  only  the 
minor  \every  king  is  a  man"]  is  omitted,  and  left  to  the 
reader  to  supply,  as  being  a  proposition  so  familiar  and 
evident,  that  it  cannot  escape  him. 


OF  LOGIC.  159 

-  Sec.  X.  Enthymemes* 

These  seemingly  imperfect  syllogisms  are  called 
EnthymemeS)  and  occur  very  frequently  in  reasoning, 
especially  where  it  makes  a  part  of  common  conversa- 
tion. Nay,  there  is  a  particular  elegance  in  them,  be- 
cause not  displaying  the  arguments  in  all  its  parts, 
they  leave  somewhat  to  the  exercise  and  invention  of 
the  mind.  By  this  means  we  are  put  upon  exerting 
ourselves,  and  seem  to  share  in  the  discovery  of  what 
is  proposed  to  us.  Now  this  is  the  great  secret  of  fine 
writing,  so  to  frame  and  put  together  our  thoughts, 
as  to  give  full  play  to  the  reader's  imagination,  and 
draw  him  insensibly  into  our  very  views  and  course  of 
reasoning.  This  gives  a  pleasure  not  unlike  to  that 
■which  the  author  himself  feels  in  composing.  It  besides 
shortens  discourse,  and  adds  a  certain  force  and  liveli- 
ness to  our  arguments,  when  the  words  in  which  they 
are  conveyed,  favour  the  natural  quickness  of  the  mind 
in  its  operations,  and  a  single  expression  is  left  to  ex- 
hibit a  whole  train  of  thoughts. 

Sec.  XI,t;Gronnd  of  Reasoning  in    immediate  Conse* 
quences,     .  • 

But  there  is  another  species  of  reasoning  with  two' 
propositions,  which  seems  to  be  complete  in  itself,  and 
where  we  admit  the  conclusion,  without  supposing  any  . 
tacit  or  suppressed  judgment  in  the  mind,  from  which 
it  follows  syllogisticaliy.  This  happens  between  pro-  . 
positions  where  the  connexion  is  such,  that  the  admis- 
sion of  the  one,  necessarily,  and  at  the  first  sight,  im- 
plies the  admission  also  of  the  other.  '  For  if  it  so  falls 
out,  that  the  proposition,  on  which  the  other  depends,  is 
self-evident,  we  content  ourselves  with  barely  affirm- 
ing it,  and  infer  that  other  by  a  direct  conclusion. 
Thus,  by  admitting  an  universal  proposition,  we  are 
forced  also  to  admit  of  all  the  particular  propositions 
comprehended  under  it,  this  being  the  very  condition 
that  constitutes  a  proposition  universal.  If  then  that 
universal  proposition  chances  to  be  self-evident,  the 
particular  ones  follow  of  course,  without  any  farther 
train    of  reasoning.     Whoever  allows,  for   instance, 


160  DUNCAN'S  ELEMENTS 

that  things  equal  to  one  and  the  same  thing  are  equal  t& 
one  another,  must  at  the  same  time  allow,  that  two  tfr/- 
angles,  each  equal  to  a  square,  whost  side  is  three 
inches,  are  also  equal  between  themselves.  This  argu- 
ment therefore, 

Things  equal  to  one  and  the  same  thing,  are  equal  to  on* 
another; 

Therefore  those  two  triangles,  each  equal  to  the  square  of 
a  line  of\three  inches,  are  equal  between  themselves  ; 
is  complete  in  its  kind,  and  contains  all.  that  is  neces- 
sary towards  a  just  and  legitimate  conclusion.  For  the 
Jirst  or  universal  proposition  is  self-evident,  and  there- 
fore requires  no  farther  proof.  And  as  the  truth  of  the 
particular  is  inseparably  connected  with  that  of  the 
universal,  it  follows  from  it  by  an  obvious  and  una- 
voidable consequence. 

Sec.    XI J... .All    reducible  to   Syllogisms   of  some  one 
form  or  other. 

Now  in  all  cases  of  this  kind  where  propositions  are 
deduced  one  from  another,  on  account  of  a  known  and 
evident  connexion,  ye  are  said  to  reason  by  immediate 
consequence.  Such  a  coherence  of  propositions,  mani- 
fest at  first  sight,  and  forcing  itself  upon  the  mind,  fre- 
quently occurs  in  reasoning.  Logicians  have  explain- 
ed at  sorse  leangth,  the  several  suppositions  upon  which 
it  takes  place,  and  allow  of  all  immediate  consequences 
that  follow  in  conformity  to  them.  It  is,  however, 
•observable,  that  these  arguments,  though  seemingly 
Complete,  because  '  the  conclusion  follows  necessarily 
from  the  single  proposition  that  goes  before,  may  yet 
be  considered  as  real  enlhjmemes,  whose  major,  which 
is  a  conditional  proposition,^  wanting.  The  syllo- 
gism but  just  mentioned,  when  represented  according 
to  this  view,  will  run  as  lollows  : 

If  things  equal  to  one  and  the  same  thing  are  equal  to  one 
another;    these   two   triangles,   each  equal  to   a  square 
whose  side  is  three  inches,  are  also  equal  between  them- 
selves. 
But  things  equal  to  one  and  the  same  thing,  arejequal  to 

one  another; 
Therefore  also  these  triangles,   &c.  are   espial  between 
themselves. 


OF  LOGIC.  161 

This  observation  will  be  found  to  hold  in  all  immedi- 
ate consequences  whatsoever,  insomuch  that  they  are 
in  fact  no  more  than  enthymemes  of  hypothetical  syl- 
logisms. But  then  it  is  particular  to  them,  that  the 
ground,  on  which  the  conclusion  rests,  namely,  its  co- 
herence with  the  minor,  is  of  itself  apparent,  and  seen 
immediately  to  flow  from  the  rules  and  reasons  of  logic. 
As  it  is,  therefore,  entirely  unnecessary  to  express  a 
self-evident  connexion,  the  major,  whose  office  that  is, 
is  constantly  omitted  ;  nsy,  and  seems  so  very  little 
needful  to  enforce  the  conclusion,  as  to  be  accounted 
commonly  no  part  of  the  argument  at  all.  It  must 
indeed  be  owned,  that  the  foregoing  immediate  conse- 
quence might  have  been  reduced  to  a  simple,  as  well 
as  an  hypothetical  syllogism.  This  will  be  evident  to 
any  one  who  gives  himself  the  trouble  to  make  the  ex- 
periment. But  it  is  not  my  design  to  enter  farther  in- 
to these  niceties,  what  has  been  said  sufficing  to  show, 
that  all  arguments  consisting  of  but  two  propositions, 
are  real  enthymemes,  and  reducible  to  complete  syllo- 
gisms of  some  one  form,  or  other.  As,  therefore,  the 
ground  on  which  the  conclusion  rests>  must  needs  be 
always  the  same  with  that  of  the  syllogisms  to  which 
they  belong,  we  have .  here  an  universal  •criterion,' 
whereby  at  all  times  to  ascertain  the  justness-aad  valid- 
ity of  our  reasonings  in  this  way. 

Sec.  XIII.  ,;A  Sorites  of  plain  simple  Syllogisms, 

The  next  species  of  reasoning  we  shall  take  notice 
of  here,  is  what  is  commonly  known  by  the  .name  of  a 
sorites.  This  is  a  way  of  arguing,  in  which  a  great 
number  of  propositions  are  so  linked  together,  that  the 
predicate  of  one  becomes  continually  the  subject  of  the 
next  following,  until  at  last  a  conclusion  is  formed,  by 
bringing  together  the  subject  of  the  first  proposition 
and  the  predicate  of  the  last.  Of  this  kind  is  the  fol- 
lowing argument  : 

God  is  omnipotent, 

An  omnipotent  being  can  do  every  thing  possible, 

He  that  can  do  every  thing  possible,  can  do  whatever  in- 
volves not  a  contradiction.; 

Therefore  God  can  do  whatever  involves  net  a  contradiction. 

02 


162  DUNCAN'S  ELEMENTS 

This  particular  combination  of  propositions  may  be 
continued  to  any  length  Ave  please,  without  in  the  least 
-weakening  the  ground  upon  which  the  conclusion  rests. 
The  reason  is,  because  the  sorites  itself  may  be  resolv- 
ed into  as  many  simple  syllogisms  as  there  are  middle 
terms  in  it ;  where  this  is  found  universally  to  hold, 
that  when  such  a  resolution  is  made,  and  the  syllogisms 
are  placed  in  train,  the  conclusion  of  the  last  in  the 
series  is  also  the  conclusion  of  the  sorites.  This  kind 
of  argument,  therefore,  as  it  serves  to  unite  several  syl- 
logisms into  one,  must  stand  upon  the  same  foundation 
with  the  syllogisms  of  which  it  consists  ;  and  is,  in- 
deed, properly  speaking,  no  other  than  a  compendious 
way  of  reasoning  syllogistically.  Any  one  maybe  sa- 
tisfied of  this  at  pleasure,'  if  he  but  takes  the  trouble  of 
resolving  the  foregoing  sorites  into  two  distinct  syllo- 
gisms,. For  he  will  there  find,  that  he  arrives  at  the 
same  conclusion,  and  that,  too,  by  the  very  same  train 
©f  thinking,  but  with  abundantly  more  words,  and  the 
addition  of  two  superfluous  propositions. 

Sec.  XIV....  6  Sorites  of  Hypothetical  Syllogisms, 

What  is  here  said  of  plain  simple  propositions,  may 
be  well  applied  to  those  that  are  conditional  ;  that  is, 
any  number  of  them  may  be  so  joined  together  in  a 
series,  that  the  consequent  of  one,  shall  become  contin- 
ually the  antecedent  of  the  next  following  ;  in  which 
case,  by  establishing  the  antecedent  of  the  first  propo- 
sition, we  establish  the  consequent  of  the  last,  or  by 
removing  the  last  consequent,  remove  also  the  first  an- 
tecedent. This  way  of  reasoning  is  exemplified  in  the 
following  argument : 

If  we  love  any  person,  all  emotions  of  hatred  towards  him 
cease. 

If  all  emotions  of  hatred  towards  a  person  cease,  we  cannot 
rejoice  in  his  misfortunes. 

If  we  rejoice  not  in  his  misfortunes,  we  certainly  wish 
him  no  injury. 

Therefore  if  we  love  a  person,  we  wish  him  no  injury. 
It  is  evident  that  this  sorites,  as  well  as  the  last,  may- 
be resolved  into  a   series  of  distinct  syllogisms,   with 
this  only  difference,  that  here  the  sylk  Tisms  are  all  con- 


OF  LOGIC.  163 

ditional.  But  as  the  conclusion  of  the  last  syllogism  in 
the  series  is  the  same  with  the  conclusion  of  the  sorites, 
it  is  plain,  that  this  also  is  a.  compendious  way  of  rea- 
soning, whose  evidence  arises  from  the  evidence  of  the 
several  single  syllogisms  into  which  it  may  be  resolved. 

Sec.  XV....77ie  Ground  of  Reasoning  by  Induction. 
I  come  now  to  that  kind  of  argument,  which  logici- 
ans call  induction;  in  order  to  the  right  understanding 
of  which,  it  will  be  necessary  to  observe,  that  our  ge- 
neral ideas  are  for  the  most  part  capable  of  various  sub- 
divisions. Thus  the  idea  of  the  Lowest  species  may  be 
subdivided  into»its  several  individuals ;  the  idea  of  any 
genus,  into  the  different  species  it  comprehends ;  and 
so  of  the  rest.  If  then  we-suppose  this  distribution  to 
be  duly  made,  and  so  as  to  take  in  the  whole  extent  of 
the  idea  to  which  it  belongs  ;  then  it  is  plain,  that  all 
the  subdivisions  or  parts  of  any  idea  taken  together  con- 
stitute tha*  whole  idea.  Thus  the  several  individuals 
of  any  species  taken  together  constitute  the  whole  spe- 
cies, and  all  the  various  species  comprehended  under 
any  genus,  make  up  the  whole  genus.  This  being  allow- 
ed, it  is  apparent,  that  whatsoever  may  be  affirmed  of 
all  the  several  subdivisions  and  classes  of  any  idea, 
ought  to  be  affirmed  of  the  whole  general  idea  to  which 
these  subdivisions  belong.  What  may  be  affirmed  of 
all  the  individuals  of  any  species,  may  be  affirmed  of  the 
whole  species ;  and  what  may  be  affirmed  of  all  the 
species  of  any  genus,  may  also  be  affirmed  of  the  whole 
genus ;  because  all  the  individuals,  taken  together,  are 
the  same  with  the  species,  and  all  the  species  taken  to- 
gether, the  same  with  the  genus. 

Sec.  XVI The  Form  and  Structure  of  an  Argu« 

ment  by  Induction. 
This  way  of  arguing,  where  we  infer  universalfy 
concerning  any  idea,  what  we  had  before  affirmed  or 
denied  separately,  of  all  its  several  subdivisions  ancj. 
parts,  is  called  reasoning  by  induction.  Thus  if  we  sup- 
pose the  whole  tribe  of  animals,  subdivided  into  men, 
beasts,  birds,  insects,  and  fishes,  and  then  reason  con- 
cerning   them   after  this   manner  :  All  men    have  a 


164  DUNCAN'S  ELEMENTS 

power  of  beginning  motion  ;  all  beasts,  birds,  and  in* 
sects,  have  a  power  of  beginning  motion  ;  all  fishes 
have  a  power  of  beginning  motion  ;  therefort  ail  ani- 
mals have  a  power  of  beginning,  motion  :  The  argu- 
ment is  an  induction*  When  the  subdivisions  are  just, 
so  as  to  take  in  the  whole  general  idea,  and  the  enu- 
meration is  perfect,  that  is,  extends  to  all  and  every  of 
the  inferior  classes  or  parts  ;  there  the  induction  is 
complete,  and  the  manner  of  reasoning^  by  induction 
is  apparently  conclusive,' 

Sec,  XVII....  The  Ground  of  Argumentation  in  a  Di- 
lemma* 

The  last  species  of  syllogisms  I  shall  take  notice  of, 
in  this  chapter,  is  that  commonly  distinguished  by  the 
name  of  a  dilemma,  A  dilemma  is  an  argument  by 
which  we  endeavour  to  prove  the  absurdity  or  falsehood  * 
of  some  assertion.  In  order  to  this  we  assume  a  con- 
ditional proposition  ;  the  antecedent  of  which  is  the  as- 
sertion to  be  disproved  and  the  consequent  a  disjunc- 
tive proposition,  enumerating  all  the  possible  suppo- 
sitions upon  which  that  assertion  can  take  place.  If 
then  it  appears,  that  all  these  several  suppositions 
ought  to  be  rejected,  it  is  plain,  that  the  antecedent,  or 
assertion,  itself,  must  be  so  too.  When,  therefore, 
such  a  proposition  as  that  before-mentioned,  is  made 
the  major  of  any  syllogism — if  the  minor  rejects  all 
the  -suppositions  contained  in  the  consequent,  it  fol- 
lows necessarily,  that  the  conclusion  ought  to  reject 
the  antecedent,  which,  as  we  have  said,  is  the  very  as- 
sertion to  be  disproved.  This  particular  way  of  ar- 
guing, is  that  which  logicians  call  a  dilemma  ;  and 
from  the  account  here  given  of  it,  it  appears,  that  we 
may  in  general  define  it  to  be  an  hypothetical  syllogism, 
where  the  consequent  of  the  major  is  a  disjunctive  pro- 
position,  which  is  wholly  taken  away  or  removed  in  the 
minor.     Of  this  kind  is  the  following  : 

If  God  did  not  create  the  world  perfect    in   its   kind,   it 

must  either  proceed  from  want  of  inclination,   or  from 

want  of  power. 
But  it  could  not  proceed  either  from  want  of  inclination, 

or  from  want  of  power. 


OF  LOGIC.  16S 

Therefore  he  created  the  world  perfect  in  its  kind.  Or 
nvbicb  is  the  same  thing :  'Tis  absurd  to  say  that  he  did  not 
create  the  world  perfect  in  its  kind. 

Sec.  XVIII... ,An  universal  Description  of  it. 

The  nature  then  of  a  dilemma  is  universally  this* 
The  major  is  a  conditional  proposition,  whose  conse- 
quent contains  all  the  several  suppositions  upon  which 
the  antecedent  can  take  place.  As,  therefore,  these 
suppositions  are  wholly  removed  iathe  minor  ^  it  is 
evident,  that  the  antecedent  must  be  so  too  ;  insomuch 
that  we  here  always  argue  from  the  removal  of  the 
consequent  to  the  removal  ^f  the  antecedent.  That 
is,  a  dilemma  is  an  argument,  in  the  modus  tollens  of 
hypothetical  syllogisms,  as  logicians  love  to  speak. 
*Hence  it  is  plain,  that'if  the  antecedent  of  the  major 
is  an  affirmative  proposition,  the  conclusion  of  the  .di- 
lemma will  be  negative  ;  but  if  it  is  a  negative  propo- 
sition, the  conclusion  will  be  affirmative.  I  cannot 
dismiss  the  subject  without  observing*,  that  as  there,  is 
something  very  curious  and  entertaining  in  the  struc- 
ture of  a  d He  mm  a ,  so  is  it  a  manner  or  reasoning  that 
occurs  frequently  in  mathematical  demonstrations. 
Nothing  is  more  common  with  Euclid,  when  about  to 
show  the  equality  of  two  given  figures,  or,  which  is  the 
same  thing,  to  prove  the  absurdity  of  asserting  them 
unequal  ;  nothing,  I  say,  is  more  cqmmon  with  him, 
than  to  assume,  that  if  the  one  is  not  equal  to  the  other9 
it  must  be  either  greater  or  less  :  and  having  destroy- 
ed both  these  suppositions,  upon  which  alone  .the  asser- 
tion can  stand,  he  thence  very  naturally  inters,  that  the 
assertion  itself  is  false.  Now  this  is  precisely  the  rea- 
soning of  a  dilemma,  and  in~e very  step'  coincides  with 
the  frame  and  composition  of  that  argument,  as  w« 
have  described  it  above» 


DUNCAN'S  ELEMENTS 

— «w»  •#  ©  ■»  tarn- 

<5Pjbap,  V. 

OF  DEMONSTRATION. 

Sec.  I....0/" Reason'mgby  a  Concatenation  of  Syllogisms* 

HAVING  dispatched  what  seemed  necessary  to  be 
said  with  regard  to  the  forms  of  syllogisms,  we 
now  proceed  to  supply  their  use  and  application  in  rea- 
soning.     We    have  seen,  that  in  all  the  different  ap- 
pearances they  put  on,   we  still  arrive  at  a  just  and  le- 
gitimate conclusion.      Now  it  often  happens,  that  the 
conclusion    of  one   syllogism  becomes  a  previous  pro- 
position in  another,  by  which  means  great  numbers  of 
them  are    sometimes  linked   together  in  a  series,    and 
truths  are  made  to  follow  one  another-in  train.     And 
as  in  such  a  concatenation  of  syllogisms,  all  the  van- 
Cm  s  ways  of  reasoning  that  are  truly  conclusive,  may  be 
■with    safety  introduced  ;   hence  it  is  plain,  that  in  de- 
ducing   any   truth  from  its  first  principles,    especially 
■when  it  lies  at  a  considerable  distance  from  them,  we 
are  at-libertyto  combine  all  the  several  kinds  of  argu- 
ments above  explained,  according  as  they  are  found  best 
to  suit  the  end  and  purpose  of  our  enquiries.      When  a 
proposition  is  thus,  by  means  of  syllogisms,  collected 
from  others  more  evident  and  known,    it  is  said  to  be 
proved  ;  so  that  we  may  in  the  general  define  the  proof 
of  a  proposition,  to  be  a  syllogism,   or  series  of  syllo- 
gisms, collecting  that  proposition  from  known  and  evi- 
dent truths.     But  more  particularly,  if  the  syllogisms, 
of  which  the  proof  consists,  admit  of  no  premises  but 
definitions,  self-evident  truths,  and  propositions  alrea- 
dy established,  then  is  the  argument  so  constituted  cal- 
led a  demonstration  ;  whereby  it  appears,  that  demon- 
strations are  ultimately  founded  on  definitions  and  self- 
evident  propositions. 

Sec.   II.. ..All Syllogisms  whatsoever  Reducible  to  the 

first  Figure. 
But  as  a  demonstration  oft-times  consists  of  a  long 


OF  LOGIC.  167 

chain  of  proofs,  where  all  the  various  ways  of  arguing 
have  place,  and  where  the  ground  of  evidence  must  o£ 
ceurse  be  diffenfnt  in  different  parts,  agreeably  to  the 
form  of  the   argument  made  use  of;    it  may  not  per- 
haps be  unacceptable,  if  we  here  endeavour  to  reduce 
the  evidence  of  demonstration  to  one  simple  principle, 
whence,  as  a  sure  and  unalterable  foundation,  the  cer- 
tainty of  it  may  in  all  cases  be  derived.     In  order  to 
this  we  must  first  observe,  that  all  syllogisms  whatso- 
ever, whether  compound,  multiform,  or  defective,  are 
reducible  to  plain  simple  syllogisms  in  some  one  of  the 
four  figures.      But  this  is  not  all.     Syllogisms  of  the 
first  figure  in  particular   admit  of  all  possible    conclu- 
sions :  that  is,  any  proposition  whatsoever,  whether  an 
universal  affirmative,  or  universal  negative,  a  particu- 
lar affirmative  or  particular  negative,   (which  fourfold 
division,  as  we  have  already  demonstrated  in  the  second 
part,  embraces  all  their  varieties)  any  one,    I  say,  of 
these  may  be  inferred,  by  virtue  of  some  syllogism  in 
the  first  figure.     By  this  means  it  happens,  that  the  syl- 
logisms of  all   the  other  figures  are   reducible  also  to 
syllogisms  of  the  first  figure,  and  may  be  considered  as 
standing  on  tht  same  foundation  with  them.  We  cannot 
here  demonstrate  and  explain  the  manner  ©f  this  re- 
duction, because  it  would  too  much  swell  the  bulk  of 
this   treatise.       It  is  enough  to  take  notice,  that  the 
thing  is  universally  known  and  allowed  among  logici- 
ans, to-  whose  writings  we  refer  such  as  desire  farther 
satisfaction  in  this  matter.     This  then  being  laid  down, 
it  is  plain,  that  any  demonstration  whatsoever  may  be 
considered~as  composed  of  a  series  of  syllogisms,  all  in 
the  first  figure.     For  since  all  the  syllogisms,  that  en- 
ter the  demonstration,  are  reduced  to  syllogisms  of  some 
one  of  the  four  figures,  and  since    the   syllogisms  of 
ail  the  other  figures  are  farther  reducible  to  syllogisms 
of  the  first  figure,  it  is  evident,  that  the  whole  demon- 
stration-may be  resolved  into  a  series  of  these  last  syl- 
logisms.    Let  us  now,  if  possible,  discover  the  ground 
upon  which  the  conclusion  rests,  in  syllogisms  of  the 
first  figure  ;  because,  by  so  doing,  we  shall  come  at  an 
universal  principle  of  certainty,  whence  the  evidence 


163  DUNCAN'S  ELEMENTS 

of  all  demonstrations,  in  all  their  parts,  may  be  ulti- 
mately derived. 

Sec.  HI*...  The  ground  of  Reasoning  in  the  first  Figure, 
The  rules  then  of  the  first  figure  are  briefly  these. 
The  middle  term  is  the  subject  of  the  major  proposi- 
tion, and  the  predicate  of  the  minor.  The  major  is  al-, 
ways  an  universal  proposition,  and  the  minor  always 
affirmative.  Let  us  now  see  what  effect  these  rules 
will  have  in  reasoning".  The  major  is  an  universal  pro- 
position, of  which  the  middle  term  is  the  subject,  and 
the  predicate  of  the  conclusion  the  predicate.  Hence 
it  appears,  that  in  the  major,  the  predicate  of  the  con- 
elusion  is  always  affirmed  or  denied  universally  of  the 
middle  term.  Again,  the  minor  is  an  affirmative  pro- 
position, whereof  the  subject  of  the  conclusion  is  the  sub- 
ject, and  the  middle  term  the  predicate.  Here  then 
the  middle  term  is  affirmed  of  the  subject  of  the  con- 
elusion  :'  that  is,  the  subject  of  the  conclusion  is  affirmed 
to  be  comprehended  under,  or  to  make  apart  of  the  mid* 
die  term.  Thus  then  we  see  what  is  done  in  thepremises 
of  a  syllogism  of  the  first  figure.  The  predicate  of  the 
conclusion  is  universally  affirmed  or  denied  of  some  idea. 
The  subject  of  the  conclusion  is  affirmed  to  be,  or  to 
make  a  partof  that  idea.  Hence  it  naturally  and  una- 
voidably follows,  that  the  predicate  of  the  conclusion 
ought  to  be  affirmed  or  denied  of  the  subject.  To 
illustrate  this  by  an  example,  we  shall  resume  one  of 
the  syllogisms  of  the  first  chapter : 

Every  creature,  possessed  of  reason  and  liberty,  is  account- 
able for  his  actions. 
Man  is  a  creature  possessed  of  reason  and  liberty  : 
Therefore  man  is  accountable  for  his  actions. 
Here,  in  the  first  proposition,  the  predicate  of  the 
conclusion,  aecountableness,  is  affirmed  of  all  creatures 
that  have  reason  and  liberty.      Again,  in  the  second 
proposition,  man,  the  subject  of  the  conclusion,  is  af- 
firmed to  be,  or  to  make  a  part  of  this  class  of  creatures. 
Hence  the  conclusion  necessarily  and  unavoidably  fol- 
lows, viz.  that  man  is  accountable  for  his  actions.  I  say 
this  follows  necessarily  and  unavoidably.     Because,  if 
reason  and  liberty  be  that  which  constitutes  a  creature 


OF  LOGIC.  169 

accountable,  and  man  has  reason  and  liberty,  it  is  plain 
-  he  has  that  which  constitutes  him  accountable*  In  like 
manner,  -where,  the  major  is  a  negative  proposition,  or 
denies  the  predicate  of  the  conclusion  universally  of  the 
middle  term  ;  as  the  minor  always  asserts  the  subject 
of  the  conclusion  to  be  or  make  a  part  of  that  middle 
term,  it  is  no  less  evident,  that  the  predicate  of  the 
conclusion  ought  in  this  case  to  be  denied  of  the  sub- 
ject. So  that  the  ground  of  reasoning,  in  all  syllo- 
gisms of  the  first  figure,  is  manifestly  this  :  Whatever 
may  be  affirmed  universally  of  any  idea,  may  be  affirm- 
ed of  every  or  any  number  of  particulars  comprehended 
wider  that  idea*  And  again  :  Whatever  may  be  deni~ 
ed  universally  of  any  idea,  may  be  in  like  manner  deni- 
ed of  every  or  any  number  of  its  individuals.  These 
two  propositions  are  called  by  logicians  the  dictum  de 
omni,  and  dictum  de  nullo,  and  are  indeed  the  great 
principles  of  syllogistic  reasoning  ;  inasmuch  as  all 
conclusions  whatsoever,  either  rest  immediately  upon 
them,  or  upon  propositions  deduced  from  them.  But 
what  adds  greatly  to  their  value  is,  that  they  are  really 
self-evident  truths,  and  such  as  we  cannot  gainsay, 
without  running  into  an  express  contradiction.  To 
affirm,  for  instance,  that  no  man  is  perfect,  and  yet  ar- 
gue that  that  some  men  are  perfect  ;  or  to  say  that  all 
men  are  mortal,  and  yet  that  some  men  are  not  mortal,  is 
to  assert  a  thing  to  be  and  not  to  be  at  the  same  time. 

Sec.  IV ., ..Demonstration,  an  Infallible  Guide  to  Truth 
and  Certainty. 

And  now  I  think  we  are  sufficiently  authorized  to 
affirm j  that  in  all  syllogisms  of  the  first  figure,  if  the 
premises  are  true,  the  conclusion  must  needs  be  true. 
If  it  be  true  that  the  predicate  of  the  conclusion,  whe- 
ther affirmative  or  negative,  agrees  universally  to  some 
idea.... and  if  it  be  also  true,  that  the  subject  of  the 
conclusion  is  a  part  of  or  comprehended  under  that  idea  ; 
then  it  necessarily  follows,^  that  the  predicate  of  the 
conclusion  agrees  also  to  the  svdject.  Fcr  to  assert  the 
contrary,  would  be  to  run  counter  to  some  one  of  the 
two  principles  before  established  j  that  is5.it  would  be 
P 


170  DUNCAN'S  ELEMENTS 

to  maintain  an  evident  contradiction.  And  thus  we 
are  come  at  last  to  the  point  we  have  been  all  along  en- 
deavouring to  establish ;  namely,  that  every  proposi- 
tion, which  can  be  demonstrated,  is  necessarily  true. 
For  as  every  demonstration  may  be  resolved  into- a  se- 
ries of  syllogisms,  all  in  the  first  figure,  and  as  in  any 
one  of  these  syllogisms,  if  the  premises  are  true,  the 
conclusion  must  needs  be  sp  too  :  it  evidently  follows, 
that  if  all  the  several  premises  are  true,  all  the  several 
conclusions  are  so,  and  consequently  the  conclusion  al- 
so of  the  last  syllogism,  which  is  always  the  proposition 
to  be  demonstrated.  Now  that  all  the  premises  of  a 
demonstration  are  true,  will  easily  appear,  from  the  ve- 
ry nature  and  definition  of  that  form  of  reasoning.  A 
demonstration,  as  we  have  said,  is  a  series  of  syllogisms, 
all  whose  premises  are  either  definitions,  self-evident 
truths,  or  propositions  already  established.  Definitions 
are  identical  propositions,  wherein  we  connect  the  des- 
cription of  an  idea  with  the  name  by  which  we  choose 
to  have  that  idea  called  ;  and  therefore  as  to  their 
truth  there  can  be  no^kjspute.  Self-evident  propositi- 
ons appear  true  of  themselves,  and  leave  no  doubt  or 
uncertainty  in  the  mind.  Propositions  before  esta- 
blished, are  no  other  than  conclusions,  gained  by  one 
or  more  steps  from  definitions  and  self-evident  princi- 
ples ;  that  is,  from  true  premises,  and  therefore  must 
Beeds  be  true.  Wl;ence  all  the  previous  propositions 
of  a  demonstration,  being,  we  sec,  manifestly  true,  the 
last  conclusion,  or  proposition  to  be  demonstrated,  mus  t 
be  so  too.  So  that  demonstration  not  only  leads  to  cer- 
tain truth,  but  we  have  here  a  clear  view  of  the  ground 
and  foundation  of  that  certainty.  For  as  in  demonstrat- 
ing, we  may  be  said  to  do  nothing  more  than  combine 
a  series  of  syllogisms  together,  all  resting  on  the  same 
bottom;  it  is  plain,  that  one  uniform  ground  of  cer- 
tainty runs  though  the  whole,  and  that  the  conclusions 
are  every  where  built  upon  some  one  of  the  two  prin- 
ciples before  established,  as  the  foundation  of  all  our 
reasoning.  These  two  principles  are  easily  reduced  in- 
to one,  and  may  be  expressed  thus  :  Whatever  predicate, 
whether  affirmative  or  negative,  agrees  universalij  to 


OF  LOGIC.  in 

cny  idea^  the  same  must  needs  agree  to  every  or  any 
number  of  individuals  comprehended  under  that  idea* 
And  thus  at  length  we  have,  according  to  our  first  de- 
sign, reduced  the  certainty  of  demonstration  to  one  sim- 
ple and  universal  principle  which  carries  its  own  evidence 
along  with  it  and  which  is,  indeed,  the  ultimate  foun- 
dation of  all  syllogistic  reasoning. 

Sec.  V.  The  rules  of  Logic  furnish  a  sufficient  criterion 
for  the  distinguishing  between  Truth  and  Falsehood. 

Demonstration,  therefore,  serving  as  an  infallible 
guide  to  truth,  and  standing  on  so  sure  and  unaltera- 
ble a  basis,  we  may  now  venture  to  assert,  what  I  doubt 
not  will  appear  a  paradox  to  many  ;  namely,  that 
the  rules  of  logic  furnish  a  sufficient  criterion  for  the 
distinguishing  between  truth  and  falsehood.  For  since 
every  proposition  that  can  be  demonstrated  is  necessa- 
rily true,  he  is  able  to  distinguish^  truth  from  false- 
hood, who  can  with  certainty  judge  when  a  proposition 
is  duly  demonstrated.  Now  a  demonstration  is,  as  we 
have  said,  nothing  more  than  a  concatenation  of  syl- 
logisms, all  whose  premises  are  definitions,  self-evi- 
dent truths,  or  propositions  previously  established* 
To  jui^e,  therefore,  of  the  validity  of  a  demonstration^ 
we  must  be  able  to  distinguish  whether  the  definitions 
that  enter  it  are  genuine,  ana  truly  descriptive  of  the 
ideas  they  are  meant  to  exhibit  ;  whether  the  proposi- 
tions assumed  without  proof  as  intuitive  truths,  have 
really  that  self-evidence  to  which  they  lay  claim  ; 
whether  the  syllogisms  are  drawn  up  in  due.  form,  and 
agreeable  to  the  laws  of  argumentation  ;  in  fine,  whe- 
ther they  are  combined  together  in  a  just  and  orderly 
manner,  so  that  no  demonstrable  propositions  serve  any 
where  as  premises,  unless  they  are  conclusions  of  pre- 
vious syllogisms.  Now  it  is  the  business  of  logic,  in 
explaining  the  several  operations  of  the  mind,  fully  to 
instruct  us  in  all  these  points.  It  teaches  the  nature 
and  end  of  definitions,  and  lays  down  the  rules  by  which 
they  ought  to  be  framed.  It  unfolds  the  several  spe- 
cies of  propositions,  and  distinguishes  the  self-evident 
from  the  demonstrable.     It  delineates  also  the  differ- 


172  DUNCAN'S  ELEMENTS 

cnt  forms  of  syllogisms,  and  explains  the  laws  of  argn- 
mentation  proper  to  each.  In  fine,  it  describes  the  ' 
manner  ©f  combining  syllogisms,  so  as  that  they  may 
form  a  train  of  reasoning,  and  lead  to  the  successive 
discovery  of  truth.  The  precepts  of  logic,  therefore, 
as  they  enable  us  to  judge  with  certainty,  when  a  pro- 
position is  duly  demonstrated,  furnish  a  sure  criterion 
for  distinguishing  between  truth  and  falsehood. 

Sec,  VI,,.. And  extending  to  all  Cases  where  a  certain 
Knowledge  of  Truth  is  attainable. 

But  perhaps  it  maybe  objected,  that  demonstration 
is  a  thing  very  rare  and  uncommon,  as  being  the  pre* 
rogative  of  but  a  few  sciences,  and  therefore  the  crite- 
rion here  given  can  be  of  no  great  use.  I  answer,  that 
-wherever  by  the  bare  contemplation  of  our  ideas,  truth 
is  discoverable,  there  also  demonstration  may  be  ob- 
tained. Now  that  I  think  is  an  abundantly  sufficient 
criterion,  which  enables  us  to  judge  with  certainty, 
in  all  cases  where  the  knowledge  of  truth  comes  with- 
in our  reach  ;  for  with  discoveries  that  lie  beyond  the 
limits  of  the  human  mind,  we  have  properly  no  business 
nor  concernment.  *When  a  proposition  is  demonstra- 
ted, we  are  certain  0f  its  truth.  When,  on  the  con- 
trary, our  ideas  are  such  as  have  no.  visible  connexion 
nor  repugnance,  and  therefore  .furnish  not  the  proper 
means  of  tracing  their  agreement  or  disagreement, 
there  we  are  sure  that  knowledge,  scientifical  know- 
ledge 1  mean,  is  not  attainable.  But  where  there  is 
some  foundation  of  reasoning,  which  yet  amounts  not 
to  the  full  evidence  of  demonstration,  there  the  pre- 
cepts of  logic,  by  teaching  us  to  determine  aright  of 
the  degree  of  proof,  and  of  what  is  still  wanting  to 
render  it  full  and  complete,  enable  us  to  make  a  due 
ettimate  of  the  measures  of  probability,  and  to  propor- 
tion our  cssent  to  the  grounds  en  which  the  proposi- 
tion stands.  And  this  is  all  we  can  possibly  arrive  at, 
or  even  so  much  as  hope  for,  in  the  exercise  of  facul- 
ties so  imperfect  and  limited  as  ours.  For  it  were 
the  height  of  folly,  to  expect  a  criterion  that  should 
enable  us   to    distinguished    truth  from   falsehood,  ia 


OF  LOGIC.  173 

cases    where  a  certain  knowledge  of  truth  is  not  at- 
tainable. 

Sec.  Vll....The  Distinction  of  Demonstration  into  di- 
rect and  indirect. 

We  have  now  done  with  what  regards  the  ground 
and  evidence  of  demonstration  ;  but  before  we  con- 
clude this  chapter,,  it  may  net  be  improper  to  take  no- 
tice of  the  distinction  of  it  into  direct  and  indirect. 
A  direct  demonstration  is,  when  beginning  with  defi- 
nitions, self-evident  propositions,  or  known  and  allow- 
ed truths,  we  form  a  train  of  syllogisms,  and  combine 
them  in  an  orderly  manner,  continuing  the  series 
through  a  variety  of  successive  steps,  until  at  hist  wq 
arrive  at  a  syllogism,  whose  conclusion  is  the  proposi- 
tion to  be  demonstrated.  Proofs  of  this  kind  leave  no 
doubt  or  uncertainty  behind  them  ;  because  all  the  se- 
veral premises  being  true,  the  conclusions  must  be  so 
too,  and  of  course  the  very  las:  conclusion,  or  proposi- 
tion to  be  proved.  I  shall  rot,  therefore,  any  farther 
enlarge  upon  this  method  of  demonstrating  ;  having,  I 
hope,  sufficiently  explained  it  in  the  foregoing  part  of 
this  chapter,  and  shown  wherein  the  force  and  validity 
of  it  lies.  The  other  species  of  demonstration  is  the 
indirect^  or,  as  it  is  sometimes  called,  the  apclogicaL 
The  manner  of  proceeding  here  is,  by  assuming  a  pro- 
position which  directly  contradicts  that  we  mean  to 
demonstrate,  and  thence  by  a  continued  train  of  rea- 
soning, in  the  way  of  a  direct  demonstration,  deducing 
some  absurdity  or  manifest  untruth.  For  hereuj 
we  conclude  that  the  proposition  assumed  was  false, 
and  thence  again,  by  an  immediate  consequence,  that 
the  proposition  to  be  demonstrated  is  true.  1 
did,  in  his  third  book,  being  to  demonstrate,  that  cir- 
cles which  touch  one  another  inwardly  h'avf  not  the 
same  centre  ;  assumes  the  direct  contrary  to  .this,  vis. 
that  they  have  the  s,.me  centre  :  and  hence  by  an  evi- 
dent train  of  reasoning,  proves,  that  a  part  is  equal  to 
the  whole.  The  supposition  therefore  leading  to  the 
absurdity  he  concludes  to  be  false,  viz.  that  circles 
Witching  one  another  inwardly  haze  the  same  centre^ 
P  2 


174  DUNCAN'S  ELEMENTS 

and  thence   again    immediately  infers,    that  they  have 
not  the  same  centre. 

Sec,  VIII. ..Ground  of  Reasoning  in  indirect  Demon- 
strations. 
Now  because  this  manner  of  demonstration  is  ac- 
counted by  some  not  altogether  so  clear  and  satisfac- 
tory nor  to  come  up  to  that  full  degree  of  evidence, 
■which  we  meet  with  in  the  direct  way  of  proof;  I 
shall,  therefore,  endeavour  here  to  give  a  particular  il- 
lustration of  it,  and  to  show  that  it  equally  with  the 
other  leads  to  truth  and  certainty.  In  order  to  this 
"we  must  observe,  that  two  propositions  are  said  to  be 
contradictory  one  of  another,  when  that  which  is  as- 
serted to  be  in  .the  one,  is  asserted  not  to  be  in  the 
other.  Thus  the  propositions — circles  that  touch  one 
another  inwardly  have  the  same  centre — and  circles  that 
touch  one  another  inwardly  have  not  the  same  centre—^ 
are  contradictories  ;  because  the  second  asserts  the  di- 
rect contrary  of  what  is  asserted  in  the  first.  Now  in 
all  contradictory  propositions,  this  holds  universally, 
that  one  of  them  is  necessarily  true,  and  the  other  ne- 
cessarily false.  For  if  it  be  true,  that  circles,  which 
touch  one  another  inwardly,  have  not  the  same  centre, 
it  is  unavoidably  falst*,  that  they  have  the  same  centre. 
On  the  other  hand,  if  it  be  false  that  they  have  the 
same  centre,  it  is  necessarily  true,  that  they  have  not 
the  same  centre.  Since  therefore,  it  is  impossible  for 
them  to  be  both  true  or  both  false  at  the  same  time, 
it  unavoidably  follows,  that  one  is  necessarily  true,  and 
the  other  necessarily  false.  This  then  being  allowed, 
which  is  indeed  self-evident,  if  any  two  contradictory 
propositions  are  assumed,  and  one  of  them  can  by  a 
clear  train  of  reasoning  be  demonstrated  to  be  false, 
it  necessarily  follows  that  the  other  is  true.  For  as 
the  one  is  necessarily  true,  and  the  other  necessarily 
false,  when  we  come  toMiscover  which  is  the  false  pro- 
position, we  thereby  also  know  the  other  to  be  true. 

Sec.  IX... .Indirect  Demonstrations  a  sure   Guide  to 

Certainty. 
Now  this  is  pre z\"c1y  the  manner  of  an  indirect  de- 


OF  LOGIC-  173 

monstratfon,  as  is  evident  from  the  account  given  of  it 
above.  For  there  we  assume  a  proposition,  which  di- 
rectly contradicts  that  we  mean  to  demonstrate,  and 
having,  by  a  continued  series  of  proofs,  shown  it  to  be 
false,  thence  infer  that  its  contradictory,  or  the  propo- 
sition to  be  demonstrated,  is  true.  Asitherefore  this 
last  conclusion  is  certain  and  unavoidable1,  let  us  next 
enquire,  after  what  manner  we  come  to  be  satisfied  of 
the  falsehood  of  the  assumed  proposition,  that  so  no 
possible  doubt  may  remain,  as  to  the  force  and  validity 
of  demonstrations  of  this  kind.  The  manner,  then,  is 
plainly  this.  Beginning  with  the  assumed  proposition, 
we  by  the  help  of  definitions,  self-evident  truths,  or 
propositions  already  established,  continue  a  series  of 
reasoning,  in  the  way  of  a  direct  demonstration,  until 
at  length  we  arrive  at  some  absurdity  or  known  false- 
hood. _  Thus  Euclid,  in  the  example  before  mentioned, 
from  tne  supposition  that  circles  touching  one  another 
inwardly  have  the  same  centre,  deduces,  that  a  part  is 
equal- to  the  whole.  Since,  therefore,  by  a  due  and  or- 
derly process  of  reasoning,  we  come  at  last  to  a  false  con- 
clusion, it  is  manifest,  that  all  the  premises  cannot  be 
true.  For  were  all  the  premises  true,  the  last  conclu- 
sion must  be  so  too,  by  what  has  been  before  demon- 
strated. Now  as  to  all  the  other  premises  made  use  of 
in  the  course  of  reasoning,  they  are  manifest  and 
known  truths  by  supposition,  as  being  either  definitions, 
self-evident  propositions,  or  truths  established.  The 
assumed  proposition  is  that  only  as  to  which  any  doubt 
or  uncertainty  remains.  That  alone,  therefore,  can 
be  false,  and  indeed,  from  what  has  been  already  shown, 
must  unavoidably  be  so.  ,And  thus  we  see,  that  in  in- 
direct demonstrations,  two  contradictory  propositions 
being  laid  down,  one  of  which  is  demonstrated  to  be 
false,  the  other,  which  is  always  the  proposition  to  be 
proved,  must  necessarily  be  true  ;  so  that  here,  as  well 
as  in  the  direct  way  of  proof,  we  arrive  at  a  clear  and 
satisfactory  knowledge  of  truth. 

Sec,  X,..  .A  particular  Case  of  Indirect  Demonstration* 

This  is  universally  the  method  of  reasoning  in  all 


176  DUNCAN'S  ELEMENTS 

apological  or  indirect  demonstrations  ;  but  there  is  one 
particular  case,  which  has  something  so  singular  and 
curious  in  it,  that  well  deserves  to  be  mentioned  by  it- 
self; more  especially,  as  the  ground  on  which  the  con- 
clusion rests  will  require  some  farther  illustration.  It 
is,  in  short,  this :  that  if  any  proposition  is  assumed, 
from  which  in  a  direct  train  of  reasoning  we  can  deduce 
its  contradictory,  the  proposition  so  assumed  is  false, 
and  the  contradictory  one  true.  For  if  we  suppose  the 
assumed  proposition  to  be  true,  then,  since  all  the^other 
premises  that  enter  the  demonstration  are  also  true,  we 
shall  have  a  series  of  reasoning,  consisting  wholly  of 
true  premises  ;  whence  the  last  conclusion,  or  contra- 
dictory of  the  assumed  proposition,  must  be  true  like- 
wise. So  that  by  this  means  we  should  have  two  con- 
tradictory propositions  both  true  at  the  same  time, 
which  is  manifestly  impossible.  The  assumed  proposi- 
tion, therefore,  whence  this  absurdity  flows,  must  ne- 
cessarily be  false,  and  consequently  its  contradictory, 
which  is  here  the  proposition  deduced  from  it  must  be 
true.  If  then  any  proposition  is  proposed  to  be  demon- 
strated, and  we  assume  the  contradictory  of  that  pro- 
position, and  thence  directly  infer  the  proposition  to  be 
demonstrated,  by  this  very  means  we  know  that  the 
proposition  so  inferred  is  true.  For  since  from  an  as- 
sumed proposition  we  have  deduced  its  contradictory, 
we  are  thereby  certain  that  the  assumed  proposition  is 
false  ;  and  if  so,  then  its  contradictory,  or  that  deduc- 
ed from  it,  which  in  this  case  is  the  same  with  the  pro- 
position to  be  demonstrated,  mu3t  be  trim. 

Sec.  XI. ...A  due  Knowledge  of  the  Principles  of  Logic 
indispensably  necessary  to  make  us  proper  judges  ef 
Demonstration  ; 

That  this  is  not  a  mere  empty  speculation,  void  of 
all  use  and  application  in  practice,  is  evident  from  the 
conduct  of  the  mathematicians,  who  have  adopted  this 
manner  of  reasoning,  and  given  it  a  place  among  their 
demonstrations.  We  have  a  curious  instance  of  it  in 
the  twelfth  proposition  of  the  ninth  book  cf  the  ele- 
ments, Euclid  there  proposes  to  demonstrate,  that  in 


OF  LOGIC.  177 

Oiiy  series  of  numbers,  rising  fr ojn  unity  in  geometrical 
progression,  all  the  prime  numbers,  that  measure  the  last 
term  in  the  series,  will  also  measure  the  next  after  unity. 
In  order  to  this  he  assumes  the  contradictory  of  the  pro- 
position to  be  demonstrated,  namely  ;  that  some  prime 
number  measuring  the  last  term  in  the  series,  dees  not 
measure  the  next,  after  unity,  and  thence  by  a  continued 
train  of  reasoning  proves,  that  it  actually  does  measure 
it.  Hereupon  be  concludes  the  assumed  proposition  to 
be  false,  and  that  which  is  deduced  from  it,  or  its  con- 
tradictory, which  is  the  very  proposition  he  proposed 
to  demonstrate,  to  be  true.  Now  that  this  is  a  just 
and  conclusive  way  of  reasoning,  is  abundantly  mani- 
fest, from  what  we  have  so  clearly  established  above. 
I  would  only  here  observe,  how  necessary  some  know- 
ledge of  the  rules  of  logic  is,  to  enable  us  to  judge  of 
the  force,  justness,  and  validity  of  demonstrations  j 
since  siich  may  sometimes  occur,  where  the  truth  of  the 
proposition  demonstrated  will  neither  be  owned  nor 
perceived,  unless  we  know  before-hand,  by  means  of 
logic,  that  a  conclusion  so  deducea,  is  necessarily  true 
and  valid.  For  though  it  be  readily  allowed,  that  by 
the  mere  strength  of  our  natural  facultis&,  v:c  c-r,  zt 
once  discern,  that  of  two  contradictory  prepositions, 
the  one  is  necessarily  true,  and  the  other  necessarily 
false :  yet  when  they  are  so  linked  together  in  a  de- 
monstration, as  that  the  one  serves  as  a  previous  propo- 
sition, whence  the  other  is  deduced  ;  it  does  not  so  im- 
mediately appear,  without  some  knowledge  of  the  prin- 
ciples of  logic,  why  that  alone,  which  is  collected  by 
reasoning,  ought  to  be  embraced  as  true,*  and  the  other, 
whence  it  is  collected,  to  be  rejected  as  false. 

Sec.  XII....  And  of  itself  sufficient  to  guard  us  against 
Error*  and  false  Reasoning. 

Having  thus,  I  hope,  sufficiently  evinced  the  certain- 
ty of  demonstration  in  all  in  branches,  and  shown  the 
rules  by  which  we  ought  to  proceed,  in  order  to  arrive 
at  a  just  conclusion,  according  to  the  various  ways  of 
arguing  made  use  of;  I  hold  it  needless  to  enter  upon 
a  particular  consideration  of  those   several  species  of 


m  DUNCANS  ELEMENTS 

false  reasoning  which  logicians  distinguish  by  the 
name  of  sophisms.  He  that  thoroughly  understa-nds 
the  form  and  structure  of  a  good  argument,  will  of 
himself  readily  discern  every  deviation  from  it.  And 
although  sophisms  have  been  divided  into  many  classes, 
which  are  all  cailed  by  sounding  names,  that  therefore 
carry  in  them  much  appearance  of  learning  ;  yet  are 
the  errors  themselves  so  very  palpable  and  obvious, 
that  I  should  think  it  lost  labour  to  write  for  a  man 
capable  of  being  misled  by  them.  Here,  therefore,  we 
choose  to  conclude  this  third  part  of  logic,  and  shall 
in  the  next  book  give  some  account  of  method,  which, 
though  inseparable  from  reasoning,  is  nevertheless 
always  considered  by  logicians  us  a  distinct  operation 
of  the  mind;  because  its  influence  is  not  confined  to 
the  mere  exercise  of  the  reasoning  faculty,  but  extends 
in  some  degree  to  all  the  transactions  of  the  under- 
standing. 


BOOK  IV. 


OF     METHOD. 


OF  METHOD  IN  GENERAL,  AND  THE  DI- 
VISION OF  IT  INTO  ANALYTIC  AND 
SYNTHETIC. 

Sec.  I..*.  The  understanding  sometimes  employed  input- 
ting together  known  truths, 
WE  have  now  done  with  the  three  first  operations 
of  the  mind,  whose  office  it  is  to  search  after 
truth,  and  enlarge  the  bounds  of  human  knowledge. 
There  is  yet  a  fourth,  which  regards  the  disposal  and  ar- 
rangement of  our  thoughts,  when  we  endeavour  so  to 
put  them  together,   that  their  mutual  connexion  and 


OF  LOGIC.  179 

dependence  may  be  clearly  seen,  This  is  what  logicians 
call  method,  and  place  always  the  last  in  order,  in  ex- 
plaining the  powers  of  the  understanding  ;  because  it 
necessarily  supposes  a  previous  exercise  of  our  other  fa- 
culties, and  some  progress  made  in  knowledge,  before 
we  can  exert  it  in  any  extensive  degree.  It  often  hap- 
pens, in  the  pursuit  of  truth,  that  unexpected  discove- 
ries present  themselves  to  the  mind,  and  those,  too,  re- 
lating to  subjects  very  remote  from  that  about  which 
we  are  at  present  employed.  Even  the  subjects  them- 
selves of  our  enquiry,  are  not  always  chosen  with  a 
due  regard  to  order,  and  their  dependence  one  upon 
another.  Chance,  our  particular  way  of  life,  or  some 
present  and  pressing  views,  often  prompt  us  to  a  varie- 
ty of  researches,  that  have  but  little  connexion  in  the 
nature  of  things.  When,  therefore,  a  man  accustom- 
ed to  much  thinking,  comes,  after  any  considerable  in- 
terval of  time,  to  take  a  survey  of  his  intellectual  ac- 
quisitions, he  seldom  finds  reason  to  be  statisfied  with 
that  order  and  disposition,  according  to  which  they 
made  their  entrance  into  his  understanding.  They  are 
there  dispersed  and  scattered,  without  subordination, 
or  any  just  and  regular  coherence  ;  insomuch  that  the 
subserviency  of  one  truth  to  the  discovery  of  another, 
does  not  scl  readily  appear  to^the  mind.  Hence  he  is 
convinced  of  the  necessity  of  distributing  them  into 
various  classes,  and  combining  into  an  uniform  sys- 
tem whatever  relates  to  one  and  the  same  subject. 
Now  this  is  the  true  and  proper  business  of  method  ; 
to  ascertain  the  various  divisions  of  human  knowledge, 
and  so  to  adjust  and  connect  the  parts  in  every  branch* 
that  they  may  seem  to  grow  one  out  of  another,  and 
form  a  regular  body  of  science,  rising  from  first  prin- 
ciples, and  proceeding  by  an  orderly  concatenation *of 
truths. 

Sec.   11*. ..Sometimes   in  the  Search    and  Discovery  of 
such'  as  are  unknown. 

In  this  view  of  things,  it  is  plain,  that  we  must  be  be- 
forehand well  acquainted  with  the  truths  we  are  to 
combine   together ;  otherwise  how   ccuid  we  discern 


i  80  DUNCAN'S  ELEMENTS 

their  several  connexions  and  relations,  or  so  dispose  o£ 
them  as  their    mutual   dependence  may  require  ?   But 
now  it  often  happens,  the  understanding  is  employed, 
not   in  the   arrangement    and  composition    of  known 
truths,  but  in  the  search  and  discovery  of  such  as  are 
unknown.     And  here  the  manner  of  proceeding  is  very 
different,  inasmuch  as  we  assemble  at  once  our  whole 
stock  of  knowledge  relating  to  any  subject,  and,  after 
a  general  survey  of  things,  begin  with  examining  them 
separately  and  by  parts.     Hence  it  comes  to  pass,  that 
whereas   at  our  first  setting  out,    we  were  acquainted 
only  with  some  of  the  grand  strokes  and  outlines,  if  I 
may  so  say,  of  truth,  by  thus, pursuing  her  through  her 
several   windings   and  recesses^  we  gradually  discover 
those  more  inward   and  finer  touches,  whence  she  de- 
rives  all   her   strength,  symmetry  and  beauty.     And 
here  it  is,  that  when,  by  a  narrow  scrutiny  into  things, 
we  have  unravelled  any  part  of  knowledge,  and  traced 
it  to  its  first  and  original  principles,  insomuch  that  the 
whole  frame  and  contexture  of  it  lies  open  to  the  view 
of  the  mind  ;  here,  I  say,  it  is,  that,  taking  it  the  con- 
trary way,  and   beginning  with    these   principles,  we 
•can  so  adjust  and  put  together  the  parts,  as  the  order 
and  method  of  science  requires. 

Sec.  III.... Illustrated  by  the  Similitude  of  a  Watch, 

But  as  these  things  are  best  understood  when  illus- 
trated by  examples,  especially  if  they  are  obvious,  and 
taken  from  common  life  ;  let  us  suppose  any  machine, 
for  instance,  a  watch,  presented  to  us,  whose  structure 
and  composition  we  areas  yet  unacquainted  with,  but 
want,  if  possible,  to  discover.  The  manner  of  pro- 
ceeding, in  this  case,  is,  by  taking  the  whole  to  pieces, 
and  examining  the  parts  separately  one  after  another. 
When  by  such  a  scrutiny  we  have  thoroughly  inform- 
ed ourselves  of  the  frame  and  contexture  of  each,  we 
then  compare  them  together,  in  order  to  judge  of  their 
mutual  action  and  influence.  By  this  means  we  gra- 
dually trace  out  tiie  inward  make  and  composition  of 
the  whote,  and  come  at  length  to  discern,  how  parts  of 
£uch  a  form,  and  so  put  together  as  we  found,  in  unra- 


OF  LOGIC.  1S1 

veiling  and  taking  them  asunder,  constitute  that  par- 
ticular machine  called  a  watch,  and  contribute  to  all 
the  several  motions \and  phenomena  observable  in  it. 
This  discovery  being  made,  we  can  take  things  the  con- 
trary  way,  and,  beginning  with  the  parts,  so  dispose 
and  connect  them,  as  their  several  uses  and  structures 
require,  until  at  length  we  arrive  at  the  whole  itself, 
from  the  unravelling  of  which  these  parts  resulted. 

Sec,  1ST  ....Ground  of  the  Analytic  and  Synthetic  Me- 
thods. 
And  as  it  is  in  tracing  and  examining  the  works  of 
art,  so  it  is  in  a  great  measure  in  unfolding  any  part  of 
human  knowledge.  For  the  relations  and  mutual  ha- 
bitudes of  things,  do  not  always  immediately  appear, 
upbn  comparing  them  one  with  another.  Hence  we 
have  recourse  to  intermediate  ideas,  and,  by  means  of 
them,  are  furnished  with  those  previous  propositions 
that  lead  to  the  conclusion  we  are  in  quest  of.  And  if 
it  so  happen,  that  the  previous  propositions  themselves 
are  not  sufficiently  evident,  we  endeavour,'  by  new 
middle  terms,  to  ascertain  their  truth,  still  tracing 
things  backward  in  a  continued  series,  until  at  length 
we  arrive  at  some  syllogism,  where  the  premises  are 
first  snd  self-evident  principles.  This  done,  we  become 
perfectly  satisfied  as  to  the  truth  of  all  the  conclusions 
we  have  passed  through,  inasmuch  as  they  are  now  seen 
to  stand  upon  the  firm  and  immovable  foundation  of 
our  intuitive  perceptions.  And  as  we  arrived  at  this 
certainty,  by  tracing  things  backward  to  the  original 
principles  whence  they  flow,  so  may  we  at  any  time  re- 
new it  by  a  direct  contrary  process,  if,  beginning  with, 
these  principles,  we  carry  the  train  of  our  thoughts 
forward,  until  they  lead  us  by  a  connected  chain  of 
proofs,  to  the  very  last  conclusion  of  the  series. 

Sec.  V.. ..Division  of  Method  into  Analytic  and  Syn- 
thetic. 4/ 
Hence  it  appears,  that  in  disposing  and  putting  to- 
gether our  thoughts,  either  for  our  own  use,  that  the 
discoveries  we  have  made  may  at  all  times  lie  open  to 
the  review  of  the  mind  ;  or,  where  we  mean  to  com- 

Q 


182  DUNCAN'S  ELEMENTS 

municate  and  unfold  these  discoveries  to  others,  there 
are  two  ways  of  proceeding,  equally  within  our  choice. 
For  we  may  so  propose  the  truths  relating  to  any  part 
of  knowledge,  as  tliey  presented  themselves  to  the  mind 
in  the  manner  of  investigation,  carrying  on  the  series 
of  proofs  in  a  reverse  order,  until  they  at  last  termi- 
.nate  in  first  principles  :  or,  beginning  with  these  prin- 
ciples, we  take  the  contrary  way,  and  from  them  de- 
duce, by  a  direct  train  of  reasoning,  all  the  several 
propositions  we  want  to  establish.  This  diversity  in 
the  manner  of  arranging  our  thoughts  gives  rise  to  the 
twofold  division  of  method  established  among  logici- 
ans. For  method,  according  to  their  use  of  the  word, 
is  nothing  else  but  the  order  and  disposition  of  cur 
thoughts  relating  to  any  subject.  When  truths  are  so 
proposed  and  put  together,  as  they  were  or  might  have 
been  discovered,  this  is  called  the  analytic  method,  or 
the  method  of  resolution  ;  inasmuch  as  it  traces  things 
backward  to  their  source,  and  resolves  knowledge  into 
its  first  and  original  principle.  When,  on  the  other 
hand,  they  are  deduced  from  these  principles,  and  con- 
nected according  to  their  mutual  dependence,  inso- 
much that  the  truths  first  in  order  tend  always  to  the 
demonstration  of  those  that  follow,  this  constitutes 
what  we  call  the  synthetic  method,  or  method  of  compo- 
sition. For  here  we  proceed  by  gathering  together 
several  scattered  parts  of  knowledge,  and  combining 
them  into  one  whole,  or  system,  in  such  manner,  that 
the  understanding  is  enabled  distinctly  to  follow  truth 
through  all  her  different  stages  and  gradations. 

Sec.   VI.... Called  otherwise   the  Method  of  Invention 
and  the  Method  of  Science, 

There  is  farther,  to  be  taken  notice  of,  in  relation 
to  these  two  species  ©f  method  ;  that  the  first  has  also 
-obtained the  name  pf  the  method  of  invention,  because 
it  observes  the  order  in  which  our  thoughts  succeed  one 
another,  in  the  invention  or  discovery  of  truth.  The 
other,  again,  is  often  denominated  the  method  of  doc-, 
trinerar  instruction,  inasmuch  as  in  laying  our  thoughts 
before    others,  we  generally  choose  to  proceed  in  the 


OF  LOGIC.  18* 

synthetic  manner,  deducing  them  from  their  first  prin- 
ciples. For  we  are  to  observe,  that  although  there  is 
great  pleasure  in  pursuing  truth  in  the  method  of  inves- 
tigation, because  it  places  us  in  the  Condition  of  the 
inventor,  and  shows  the  particular  train  and  process  of 
thinking  by  which  he  arrived  at  his  discoveries  ;  yet  it 
is  ^not  so  well  accommodated  to  the  purposes  of  evi- 
dence and  conviction.  For  at  our  first  setting  out,  we 
are  commonly  unable  to  divine  where  the  analysis  will 
lead  us  ;  inasmuch  that  our  researches  are  for  some 
time  little  better  than  a  mere  groping  in  the  dark. 
A  nd  even  after  light  begins  to  break  in  upon  us,  we  are 
still  obliged  to  many  reviews,  and  a  frequent  compari- 
son of  the  several  steps  of  the  investigation  among 
themselves.  Nay,  when  we  have  unravelleHihe  whole, 
and  reached  the  very  foundation  on  which  our  discove- 
ries stand,  all  our  certainty,  in  regard  to  their  truth* 
will  be  found  in  a  great  measure  to  arise  from  that 
connexion  we  are  now  able  to  discern  between  them 
and  first  principles,  taken  in  the  order  of  composition* 
But  in  the  synthetic  manner  of  disposing  our  thoughts, 
the  case  is  quite  different.  For  as  we  here  begin  with 
intuitive  truths,  and  advance  by  regular  deductions 
from  them,  every  step  of  the  procedure  brings  evidence 
and  conviction  along  with  it  ;  so  that  in  our  progress 
from  one  part  of  knowledge  to  another,  we  have  al- 
ways a  clear  perception  of  the  grounds  on  which  our  as- 
sent rests.  In  communicating  therefore,  our  discove- 
ries to  others,  this  method  is  apparently  to  be  chosen, 
as  it  wonderfully  improves  and  enlightens  the  under- 
standing, and  leads  to  an  immediate  perception  of  truth. 
And  hence  it  is,  that  in  the  following  pages,  we  choose 
to  distinguish  it  by  the  name  of  the  method  of  science  ; 
not  only  as  in  the  use  of  it  we  arrive  at  science  and  cer- 
tainty, but  because  it  is  in  fact  the  method,  in  which 
all  those  parts  of  human  knowledge,  that  properly  bear 
the  name  of  sciences,  are  and  ought  to  be  delivered. 
But  we  now  proceed  to  explain  these  two  kinds  of  me- 
thod more  particularly. 


184  DUNCAN'S  ELEMENTS 


OF  THE  METHOD  OF  INVENTION. 

Sec,  I.   Origin  of  the  several  Arts   and  Inventions  of 
Human  Life, 

BY  the  method  of  invention  we  understand  such  a 
disposition  and  arrangement  of  our  thoughts,  as 
follows  the  natural  procedure  of  the  understanding,  and 
presents  them  in  the  order  in  which  they  succeed  one 
another,  in  the  investigation  and  discovery  of  truth. 
Now  it  is  plain,  that  to  handle  a  subject  successfully 
accordinggp>  this  method,  we  have  no  more  to  do  than 
observe  the  several  steps  and  advances  of  our  minds, 
and  fairly  copy  them  out  to  the  view  of  others.  And 
indeed  it  will  be  found  to  hold  in  general,  with  regard 
to  all  the  active  parts  of  human  life,  especially  when 
reduced  to  that  which  is  in  the  schools  termed  an  art ; 
that  the  rules,  by  which  we  conduct  ourselves,  are  no 
other  than  a  series  of  observations  drawn  from  the  at- 
tention of  the  mind  to  what  passes,  while  we  exercise 
our  faculties  in  that  particular  way.  For  when  we  set 
about  any  invention  or  discovery,  we  are  always  pushed 
on  by  some  inward  principle,  disposition,  or  aptitude 
shall  I  call  it,  which  we  experience  in  ourselves,  and 
•which  makes  us  believe,  that  the  thing  we  are  in  quest 
of,  is  not  altogether  beyond  our  reach.  We  therefore 
begin  with  essaying  our  strength,  and  are  sometimes 
successful,  though  perhaps  more  frequently  not.  But 
as  the  mind,  when  earnestly  bent  upon  any  pursuit,  is 
not  easily  discouraged  by  a  few  disappointments,  we  are 
only  set  upon  renewing  our  endeavours,  and*  by  an  ob- 
stinate perseverance,  and  repeated  trials,  often  arrive 
at  the  discovery  of  what  we  have  in  view.  Now  it  is 
natural  for  a  man  of  a  curious  and  inquisitive  turn,  af- 
ter having  mastered  any  part  of  knowledge  with  great 
labour  and  difficulty,  to  set  himself  to  examine  how  he 
happened  to  miscarry  in  his  first  attempts,  and  by  what 
particular  method  of  procedure  he  at  length  came  to  be 


OF  LOGIC.  185 

successful.  By  this  means  we  discover  on  the  one 
hand,  those  rocks  and  shelves  which  stand  most  in  our 
way,  and  are  apt  to  disturb  and  check  our  progress  ;  and 
on  the  ether,  that  more  sure  and  certain  course,  which 
if  we  continue  in  steadily,  will  bring  us  to  the  attain- 
ment of  what  we  are  in  pursuit  of.  Hence  spring  all 
the  arts  and  inventions  of  human  life,  which,  as  we 
l^ave  already  said,  are  founded  upon  a  series  of  rules  and 
observations,  pointing  out  the  true  and  genuine  manner 
of  arriving  at  any  attainment.  When  the  mind  res*s 
satisfieddn  a  bare  contemplation  of  the  rules,  and  the 
reasons  on  which  they  are  founded,  this  kind  of  know- 
ledgt  is  called  speculative*  But  if  we  proceed  farther, 
and  endeavour  to  apply  these  rules  to  practice,  so  as  to 
acquire  a  habit  of  exerting  them  on  all  proper  occa- 
sions, we  are  then  said  to  be  possessed  of  the  a*t  itself. 

Sec.   lf...JFhj;  in  treating  of  the  Method  of  Invention^ 
ive  must  give  ^ome  account  of  the  Art  itself 

From  what  has  been  said,  it  appears,  that,  in  order 
distinctly  to  explain  the  method  of  invention,  we  must 
take  a  view  of  the  understanding,  as  employed  in  the 
.  search  and  investigation  of  truth.  For  by  duly  attend- 
ing to  its  procedure  and  advances,  we  shall  not  only 
discover  the  rules  by  which  it  conducts  itself,  but  be 
enabled  also  to  trace  out  the  several  helps  and  contri- 
vances it  makes  use  of,  for  the  more  speedy  and  effec-' 
tual  attainment  of  its  ends*  And  when  these  particulars 
are  once  known,  it  will  not  be  difficult  for  us,  in  laying 
open  our  discoveries  to  others,  to  combine  our  thoughts 
agreeably  to  the  method  here  required.  Because,  hav- 
ing fixed  and  ascertained  the  rules  of  it,  and  being  per- 
fectly acquainted  with  the  conduct  and  manner  of  the 
mind,  we  need  only  take  a  view  of  the  several  truths, 
as  they  succeed  one  another  in  the  series  of  investiga- 
tion, set  them  in  order  before  us,  and  fairly  transcribe 
the  appearance  they  make  to  the  understanding.  Hence 
it  is,  that  logicians,  in  treating  of  the  metnod  of  in- 
vention, have  not  merely  confined  themselves  to  the 
laying  down  of  directions  for  the  disposal  and  arrange- 
ment of  our  thoughts  j  but  have  rather  explained  the 
Q2 


186  DUNCAN'S  ELEMENTS 

art  itself,  and  established  those  rules  by  which  the  mind 
ought  to  proceed  in  the  exercise  of  its  inventive  powers. 
For  they  rightly  judge,  that  if  these  were  thoroughly 
understood,  the  other  could  no  longer  remain  unknown. 
By  this  means  it  happens,  that  the  method  of  invention 
is  become  another  expression  for  the  art  of  invention, 
and  very  often  denotes  the  conduct  and  procedure  of  the 
understanding  in  the  search  of  truth.  And  as  some 
knowledge  of  the  principles  of  the  art,  is  in  a  manner 
absolutely  necessary  towards  a  true  conception  of  the 
rules  by  which  we  ought  to  govern  and  dispose  our 
thoughts  in  treating  subjects  after  this  method  ;  we 
shall,  therefore,  follow  the  example  of  other  logicians, 
and  endeavour  to  give  some  short  account  of  the  busi- 
ness of  invention,  and  of  those  several  helps  and  con- 
trivances by  which  the  mind  is  enabled  to  facilitate 
and  enlarge  its  discoveries. 

Sec.   III... .Attention  and  a  Comprehensive  understand- 
ing the  preparatory  qualifications  to  Invention, 

It  has  been  already  observed,  that  when  the  mind 
employs  itself  in  the  search  of  unknown  truths,  it  be- 
gins with  assembling  at  once  its  whole-stock  of  know- 
ledge relating  to  the  subject,  and  after  a  general  sur- 
vey of  things,  sets  about  examining  them  separately 
and  by  parts.  Now  as  in  this  separate  examination, 
the  number  of  parts  continually  increase  upon  us — and 
as  it  is  farther  necessary,  that  we  survey  them  on  all 
sides,  compare  them  one  with  another,  and  accurately 
trace  their  mutual  habitudes  and  respects — it  is  from 
hence  apparent,  that  in  the  exercise  of  invention,  two 
things  are  of  principal  consideration.  First,  an  en- 
larged and  comprehensive  understanding,  able  to  take 
in  the  great  multitude  of  particulars,  that  frequently 
come  under  our  notice.  Secondly,  a  strong  habit  of 
attention,  that  lets  nothing  remarkable  slip  its  view, 
and  distinguishes  carefully  all  those  circumstances 
which  tend  to  the  illustrating  and  clearing  the  sub- 
ject we  are  upon.  These  are  the  great  and  preparatory 
qualifications,  without  which  it  were  vain  to  hope,  that 
any  considerable  advance  could  be  made  in  enlarging 


OF  LOGIC.  187 

the  bounds  of  human  knowledge.  Nor  ought  we  to 
esteem  it  a  small  advantage,  that  they  are  in  some  mea- 
sure in  our  own  power,  and  may,  by  a  proper  cultiva- 
tion, be  improved  aud  strengthened  to  a  degree  almost 
beyond  belief.  We  find  by  experience,  that  the  study 
of:  mathematics  in  particulars  greatly  serviceable  to 
this  end.  Habits,  we  all  know,  grow  stronger  by^ex- 
ercise  ;  and  as  in  this  science  there  is  a  perpetual  call 
upon  our  attention,  it  by  degrees  becomes  natural  to 
us,  so  as  that  we  can  preserve  it  steady  and  uniform, 
through  long  and  intricate  calculations,  and  that 
with  little  or  no  fatigue  to  the"  understanding.  But  a 
yet  more  wonderful  advantage,  arising  from  the  cul- 
ture of  the  mathematics,  is  this,  that  hereby  we  in 
some  measure  extend  the  dimensions  of  the  human 
mind,  enlarge  its  compass  of  perception,  and  accustom 
it  to  wide  and  comprehensive  views  of  things.  For 
whereas  at  our  first  setting  out,  we  often  find  it  ex- 
tremely difficult  to  master  a  short  and-  easy  demon- 
stration and  trace  the  connexion  of  its  several  parts  : 
yet  as  we  advance  in  the  science,  the  understanding  is 
seen  gradually  to  dilate,  and  stretch  itself  to  a  greater 
size  ;  insomuch  that  a  long  and  intricate  series  of  rea- 
soning is  often  taken  in  with  sca«:e  any  labour  of 
thought  ;  and  not  only  so,  but  we  can  in  some  cases, 
with  a  single  glance  of  our  minds,  run  through  an  en- 
tire system  of  truths,  and  extend  our  view  at  once  to 
all  the  several  links  that  unite  and  hold  them  together. 

Sec.  IV....  "Judicious  choice  of  intermediate  Ideas  ano- 
ther great  requisite  in  this  Art. 

When  we  are  furnished  with  these  two  preparatory 
qualifications,  the  next  requisite  to  the  discovery  of 
truth  is,  a  judicious  choice  of  intermediate  ideas.  We 
have  seen,  in  the  third  part  of  this  treatise,  that  many 
of  our  ideas  are  of  such  a  nature  as  not  to  discover 
these  several  habitudes  and  relatioas  by  any  immediate 
comparison  on?  with  another.  In 'this  case,  we  must 
have  recourse  to  intermediate  ideas  ;  and  the  great  art 
lies  in  finding  out  such  as  have  an  obvious  and  perceiv- 
able connexion  with  the  ideas  whose  relations  we  en- 


188  DUNCAN'S  ELEMENTS 

quire  after.  For  thus  it  is,  that  we  are  furnished  with 
known  and  evident  truths,  to  se*ve  as  premises  for  the 
discovery  of  such  as  are  unknown.  And  indeed  the 
whole  business  of  invention  seems,,  in  a  great  measure, 
to  lie  in  the  due  assemblage  and  disposition  of  these 
preliminary  truths.  For  they  not  only  lead  us,  step 
by  step,  to  the  discovery  we  are  in  quest  of,  but  are 
so  absolutely  necessary  in  the,  case,  that  without  them 
it  were  vain  to  attempt  it ;  nothing  being  more  Cer- 
tain, than  that  unknown  propositions  can  no  otherwise 
be  traced  but  by  means  of  some  connexion  they  have 
with  such  as  are  known.  Nay,  reason  itself,  which  is 
indeed  the  art  of  knowledge,  and  the  faculty  by  which 
we  push  on  our  discoveries  ;  yet  by  the  very  definition 
of  it  implies  no  more,  than  an  ability  $f  deducing  un- 
known truths  from  principles  or  propositions  that  are 
already  known.  Now,  although  this  happy  choice  of 
intermediate  ideas,  so  as  to  iurnish  a  due  train  of  pre- 
vious propositions,  that  shall  lead  us  successively  from 
one  discovery  to  another,  depends  in  some  measure 
upon  a  natural  sagacity  and  quickness  of  mind  ;  it  is 
yet  certain,  frora  experience,  that  even  here  much  may 
be  effected  by  a  stubborn  application  and  industry.  In 
order  to  this,  it  is  in  the  first  place  necessary,  that  we 
have  an  extensive  knowledge  of  things,  and  some  ge- 
neral acquaintance  with  the  whole  circle  of  arts  and 
sciences.  Wide  and  extended  views  add  great  force 
and  penetration  to  the  mind,  and  enlarge  its  capacity 
of  judging.  And  if  to  this  we  join  in  thesecond  place, 
a  more  particular  and  intimate  study  of  whatever  re- 
lates to  the  subject  about  which  our  enquiries  are  em- 
ployed, we  seem  to  bid  fair  for  success  in  our  attempts. 
For  thus  we  are  provided  with  an  ample  variety  out  of 
which  to  choose  our  intermediate  ideas,  and  are  there- 
fore more  likely  to  discover  some  among  them  that  will 
furnish  out  the  previous  propositions  necessary  in  any 
train  of  reasoning.* 

Sec.   V.. ..Sagacity    and  a   quickness  of  understanding 
greatly  promoted  by  the  study  cf  Algebra* 

It  is  not,  indeed,  to   be  denied,  that  when  we  have 


GF  LOGIC.  189 

even  got  all  our  materials  about  us,  much  still  depends 
upon  a  certain  dexterity  and  address,  in  singling  out 
the  most  proper,  and  applying  them  skillfully  for  the 
discovery  of  truth.  This  is  that  talent  which  is  known 
by  the  name  of  sagacity,  and  commonly  supposed  to 
be  altogether  the  gift  of  nature.  But  yet  I  think  it  is 
beyond  dispute,  that  practice,  experience,  and  a  watch- 
ful attention  to  the  procedure  of  our  own  minds,  while 
employed  in  the  exercise  of  reasoning,  are  even  here  of 
very  great  avail.  It  is  a  truth  well  known  to  those 
who  have  made  any  considerable  progress  in  the  study 
of  algebra,  that  an  address  and  skill  in  managing  ^in- 
tricate questions  may  be  very  often  obtained,  by  a  care- 
ful imitation  of  the  best  models.  For  although  when  we 
first  set  out  about  the  solution  of  equations,  we  are  puz- 
zled at  every  step,  and  think  we  can  never  enough  ad- 
mire the  sagacity  of  those  who  present  us  with  elegant 
models  in  that  way  ;  yet  by  degrees  we  ourselves  ar- 
rive at  a  great  mastery,  not  only  in  devising  proper 
equations,  and  coupling  them  artfully  together,  so  as 
from  the  more  complicated  to  derive  others  that  are 
simple  ;  butaho  in  contriving  useful  substitutions,  ta 
free  our  calculations  from  fractions,  and  those  intrica- 
cies that  arise  from  surds  and  irrational  quantities; 
Nor  is  it  a  small  pleasure  attending  the  prosecution  of 
this  study,  that  we  thus  discern  the  growing  strength 
of  our  minds,  and  see,  ourselves  approaching  nearer  and 
nearer  to  that  sagacity  and  quickness  of  understand- 
ing which  we  see  so  much  admired  in  others,  and  were 
at  first  apt  to  conclude  altogether  beyond  our  reach. 

Sec.   VI Where  Art  and  Management  are  required 

in  the  business  of  invention. 

We  have  now  considered  those  requisites  to  inven- 
tion, that  have  their  foundation  in  the  natural  talents 
of  the  mind  :  and  enlarged  and  comprehensive  under- 
standing, a  strong  habit  of  attention,  a  sagacity  and 
quickness  in  discerning  and  applying  intermediate  ideas* 
Let  us  next  take  a  view  of  such  other  helps,  as  more  im- 
mediately depend  upon  art  and  management,  and  show 
the  address  of  the  mind,  in  contriving  means  to  facili- 


190  DUNCAN'S  ELEMENTS 

tate  its  discoveries,  and  free  it  from  allunnecessary  fa- 
tigue and  labour.  For  we  are  to  observe,  that  though 
the  capacity  of  the  intellect  may  be  greatly  enlarged  by 
use  and  exercise,  yet  still  our  views  are  confined  within 
certain  bounds,  beyond  which  a  finite  understanding 
cannot  reach.  And  as  it  often  happens,  in  the  inves- 
tigation of  truth,  especially  where  it  lies  at  a  consider- 
able distance  from  first  principles,  that  the  number  of 
connexions  and  relations  are  so  great,  as  not  to  be 
taken  in  at  once  by  the  most  improved  understanding; 
it  is  therefore  one  great  branch  of  the  art  of  invention, 
to  take  account  of  these  relations,  as  they  come  into 
view,  and  dispose  them  in  such  manner,  that  they  al- 
ways lie  open  to  the  inspection  of  the  mind,  when  dis- 
posed to  turn  its  attention  that  way.  By  this  means, 
-without  perplexing  ourselves  with  too  many  considera- 
tions at  once,  we  have  yet  these  relations  at  command, 
when  necessary  to  be  taken  notice  of  in  the  prosecution 
of  our  discoveries  :  and  the  understanding,  thus  free 
and  disengaged,  can  bend  its  powers  more  intensely  to- 
wards that  particular  part  of  the  investigation  it  is  at 
present  concerned  with.  Now  in  this,  according  to  my 
apprehension,  lies  the  great  art  of  human  knowledge  ; 
to  manage  with  skill  the  capacity  of  the  intellect,  and 
contrive  such  helps: as  may  bring  the  most  wide  and  -ex- 
tended objects  within  the  compass  of  its  natural  powers. 
When,  therefore,  the  multitude  of  relations  increase 
very  fast  upon  us,  and  grow  too  unwieldy  to  be  dealt 
with  in  the  lump,  we  must  combine  them  in  different 
classes,  and  so  dispose  of  the  several  parts,  as  that  they 
may  at  all  times  lie  open  to  the  leisurely  survey  of  the 
rnind.  By  this  means  we  avoid  perplexity  and  confu- 
sion, and  are  enabled  to  conduct  our  researches,  with- 
out being  puzzled  with  that  infinite  crowd  of  particu- 
lars, that  frequently  fall  under  our  notice  in  long  and 
difficult  investigations.  For  by  carrying  our  attention 
successively  from  one  part  to  another,  we  can,  upon  oc- 
casion, take  in  the  whole  ;  and  knowing  also  the  order 
and  disposition  of  the  parts,  may  have  recourse  to  any 
of  them  at  pleasure,  when  its  aid  becomes  necessary  in 
the  course  of  our  enquiries* 


OF  LOGIC.  191 

Sec.  VII. .;An  orderly  disposition  of  great  use  in 
adapting  objects  to  the  capacity  of  the  understanding ; 
First  then  I  say,  that  an  orderly  combination  of  things 
and  classing  them  together  with  art  and  address,  brings 
great  and  otherwise  unmanageable  objects,  upon  a  level 
with  the  powers  of  the  mind.-  We  have  seen,  in  the 
first  part  of  this  treatise,  how  by  taking  numbers  in  a 
progressive  series,  and  according  to  an  uniform  faw  of 
composition,  the  most  bulky  and  formidable  collections 
are  comprehended  with  ease,  and  leave  distinct  impres- 
sions in  the  understanding.  For  the  several  stages  of 
the  progression  serve  as  so  many  steps  to  the  mind,  by 
which  it  ascends  gradually  to  the  highest  combinations; 
and  as  it  can  carry  its  views  from  one  to  another,  with 
great  ease  and  expedition,  it  is  thence  enabled  to  run 
over  all  the  pnrts  separately,  and  thereby  rise  to  a  just 
conception  of  tfee  whole.  The  same  thing  happens  in 
all  our  other  complex  notions,  especially  when  they 
grow  very  large  and  complicated  ;  for  tfren  it  is  that 
we  become  sensible  of  the  necessity  of  establishing  a 
certain  order  and  gradation  in  the  manner  of  combining 
the  parts.  This  has  been  already  explained,  at  some 
length,  in  the  chapter  of  the  composition  and -resolu- 
tion of  our  ideas;  where  we  have  traced  the  gradual 
progress  of  the  mind  through  all  the  different  orders  of 
perception,  and  shown,  that  the  most  expeditious  way 
of  arriving  at  a  just  knowledge  of  the  more  compound- 
ed notices  of  the  understanding,  is  by  advancing  regu- 
larly through  all.tjie  intermediate  steps.  Hence  it  is 
easy  to  perceive  what  advantages  must  arise  from  a  like 
conduct  in  regard  to  those  several  relations  and  connex- 
ions, upon  which  the  investigation  of  truth  depends. 
For  as  by  this  means  we  are  enabled  to  bring  them  all 
within  the  reach  of  the  mind,  they  can  each  in  their 
turns  be  made  use  of  upon  occasion,  and  furnish  their 
assistance  towards  the  discovery  of  wThat  we  are  in  quest 
of.  Now  this  is  of  principal  consideration  in  the  business 
of  invention,  to  have  our  thoughts  so  much  under  com- 
mand, that,  in  comparing  things  together,  in  order  to 
discover  the  result  of  their  mutual  connexions  and  de- 
pendence, all  the  several  ligltfs  that  tend  to  the  cleariwg 


192  DUNCAN'S  ELEMENTS 

the  subject  we  are  upon,  may  lie  distinctly  open  to  the 
understanding,  so  as  nothing  material  shall  escape  its 
view  :  because  an  oversight  of  this  kind,  in  summing 
up  the  account,  must  not  only  greatly  retard  its  ad- 
vances, but  in  many  cases  check  its  progress  altogether. 

Sec.  VIII.. ,,And  enabling  us  to  proceed  gradually  and 
with  ease  in  the  investigation  of  Truth, 

.  But  secondly,  another  advantage  arising  from  this 
orderly  disposition,  is,  that  hereby  we  free  the  mind 
from  all  unnecessary  fatigue,  and  leave  it  to  fix  its  at- 
tention upon  any  part  separately,  without  perplexing  it- 
self with  the  consideration  of  the  whole.  Unknown 
truths,' as  we  have  already  ©bserved,  are  only  to  be 
traced  by  means  of  the  relation  between  them  and  others 
that  are  known.  When,  therefore,  these  relations  be- 
come very  numerous,  it  must  needs  greatly  distract  the 
mind,  were  itto  have  its  attention  continually  upon  the 
stretch  after  such  a  multitude  of  particulars  at  once. 
But  now,  by  the  method  of  classing  and  ordering  our 
perceptions  above  explained,  this  inconvenience  is 
wholly  prevented.  For  a  just  distribution  of  things,  as 
it  ascertains  distinctly  the  place  of  each,  enables  us  to 
call  any  of  them  into  view  at  pleasure,  when  the  present 
consideration  of  it  becomes  necessary.  Hence  the  mind 
proceeding  gradually  through  the  several  relations  of 
its  ideas,  and  marking  the  results  of  them  at  every  step, 
can  always  proportion  its  enquiries  to  its  strength  ;  and 
confining  itself  to  such  a  number  of  objects  as  it  can 
take  in  and  manage  with  ease,  sees  more  distinctly  all 
the  consequences  that  arise  from  comparing  them  one 
with  another.  When,  therefore,  it  comes  afterwards 
to  take  a  review  of  these  its  several  advances,  asby  this 
means  the  amount  of  every  step  of  the  investigation  is 
fairly  laid  open  to  its  inspection,  by  adjusting  and  put- 
ting these  together,  in  due  order  and  method,  it  is  en- 
abled at  last  to  discern  the  result  of  the  whole.  And 
thus,  as  before  in  the  composition  of  our  ideas  so  like- 
wise here  in  the  search  and  discovery  of  truth,  we  are 
fain  to  proceed  gradually,  and  by  a  series  of  successive 

stages.     For  these  are  so  many  resting  places  to  the 


OF  LOGIC,  193 

mind,  whence  to  look  about  it,  survey  the  conclusions 
it  has  already*  gained,  and  see  what  helps  they  afford, 
towards  the  obtaining  of  others  which  it  must  still  pass 
through,  before  it  reaches  the  end  of  the  investigation. 
Hence  it  often  happens,  that  very  remote  and  distant 
truths,  which  lie  far  beyond  the  reach  of  any  single  ef- 
fort of  the  mind,  are  yet  by,  this  progressive  method, 
successively  brought  to  light,  and  that  too  with  less  fa- 
tigue to  the  understanding  than  could  at  first  have  well 
been  imagined.  For  although  the  whole  process,  ta- 
ken together,  is  frequently  much  too  large  to  come 
within  the  view  of  the  mind  at  once  ;  and  therefore, 
considered  in  that  light,  may  be  said  truly  to  exceed 
its  grasp;  yet  the  several  steps  of  the  investigation 
by  themselves  are  often  easy  and  managable  enough, 
so  that  by  proceeding  gradually  from  one  to  another, 
and  thoroughly  mastering  the  parts  as  we  advance,  we 
carry  on  our  researches  with  wondrous  dispatch,  and 
are  at  length  conducted  to  that  very  truth,  with  a  view 
to  the  discovery  of  which  the  inquishion  itself  was  set 
on  foot. 

Sec.  IX....  Algebra  and  Arithmetic,  properly  speaking, 
both  Arts  of  Invention, 
But  now  perhaps  it  may  not  be  improper,  if  we  en- 
deavour to  illustrate  these  observations  by  an  example, 
and  set  ourselves  to  trace  the  conduct  andmanner  of 
the  mind,  when  employed  in  the  exercise  of  invention. 
There  are  two  great  branches  of  the  mathematics  pecu- 
liarly fitted  to  furnish  us  with  models  in  this  way. 
Arithmetic  I  mean,  and  Algebra.  Algebra  is  univer- 
sally known  to  be  the  very  art  and  principle  of  inven- 
tion ;  and  in  arithmetic,  too,  we  are  frequently  put 
upon  the  finding  out  of  unknown  numbers,  by  means  of 
their  relations  and  connexions  with  others  that  are 
known  :  as  where  it  is  required  to  find  a  number  equ^l 
to  this  sum  of  two  others,  or  the  product  of  two  others. 
I  choose  to  borrow  my  examples  chiefly  from  this  last 
science,  both  because  they  will  be  more  within  the 
reach  of  those  for  whom  this  treatise  is  principally  de- 
signed ;  as  likewise,  because  arithmetic  furnishes  the 
best  models  of  a  happy  sagacity  and  management,  \\\ 

R 


194  DUNCAN'S  ELEMENTS 

classing  and  regulating  our  perceptions.  So  that  here , 
more  than  in  any  other  branch  of  human  knowledge, 
we  shall  have  an  opportunity  of  observing,  how  much, 
an,  orderly  disposition  of  things  tends  to  the  ease  and 
success  of  our  enquiries,  by  leaving  us  to  canvass  the 
parts  separately,  and  thereby  rise  to  a  gradual  concep- 
tion of  the  whole,  without  entangling  ourselves  with 
too  many  considerations  at  once,  in  any  single  step  cf 
the  investigation.  For  it  will  indeed  be  found,  that  a 
dexterity  and  address,  in  the  use  of  this  last  advantage, 
serves  to  facilitate  and  promote  our  discoveries,  almost 
beyond  imagination  or  belief. 

Sec.  X....77i^  method  of  classing  our  Perceptions   in 
.    Arithmetic. 

We  have  already  explained  the  manner  of  reducing 
numbers  into  classes  and  of  distinguishing  these  clas- 
ses by  their  several  names.  And  now  we  are  farther 
to  obs#ve,  that  the  present  method  of  notation  is  so 
contrived,  as  exactly  to  fall  in  with  this  form  of  num- 
.bering.  For  as  in  the  names  of  numbers,  we  rise  irom 
units  to  tens,  from  tens  to  hundreds,  from  hundreds  to 
thousands,  ZJfc.  so  likewise  in  their  notation,  the  same 
figures,  in  different  places,  signify 'these  several  combi- 
nations. Thus  2  in  the  first  place,  on  the  right  hand 
denotes  two  units,  in  the  second  place,  it  expresses  so 
many  tens,  in  the  third  hundreds,  in  the  fourth  thou- 
sands. By  this  means  k  happens,  that  when  a  number 
is  written  down  in  figures,  as  every  figure  in  it  expresses 
some  distinct  combination,  and  all  combinations  toge- 
ther make  up  the  total  sum  ;  so  may  the  several  figures 
be  considered  as  the  constituent  parts  of  the  number. 
Thus  the  number  2436,  is  evidently,  by  the  very  no- 
tation, distinguished  into  four  parts,  marked  by  the 
four  figures  that  serve  to  express  it.  For  the  first  de- 
notes two  thousand,  the  second,  four  hundred,  the  third 
thirty  or  three  tens,  and  the  fourth  six.  These  several 
parts,  though  they,  here  appear  in  a  conjoined  form,  may 
yet  be  also  expressed  separately  thus,  2000,  400,  30, 
and  6,  and  the  amount  is  exactly  the  same. 


OF  LOGIC.  195 

Sec.  XL.*. The  helps  thence  derived  towards  an  easy 
addition  of  numbers* 
This  then  being  the  case,  if  it  is  required  to  find  a 
number  equal  to  the  sum  of  two  others  given  ;  our  bu- 
siness is,  to  examine  separately  these  given  numbers, 
and  if  they  appear  too  large  and  bulky  to  be  dealt  with 
by  a  single  elfort  of  thought,  then,  since  the  very  nota- 
tion, distinguishes  them  into  different  parts,  we  must 
content  ourselves  with  considering  the  parts  asunder, 
and  finding  their  sums  one  after  another.  For  since 
the  whole  is  equal  to  all  its  parts,  if  we  find  the  sums 
of  the  several  parts  of  which  any  two  numbers  consist, 
we  certainly  find  the  total  sum  of  the  two  numbers. 
And  therefore,  these  different  sums,  united  and  put  to- 
gether, according  to  the  established  rules  of  notation 
will  be  the  very  number  we  are  in  quest  of.  Let  it  be 
proposed  for  instance,  to  find  a  number  equal  to  the 
sum  of  these  two  :  2436,  and  4532.  As  the  finding 
of  this  by  a  single  effort  of  thought  would  be  too  vio- 
lent an  exercise  for  the  mind,  1  consider  the  figures, 
representing  these  numbers,  as  the  parts  of  which  they 
consist,  and  therefore  set  myself  to  discover  their  sums 
one  after  another.  Thus  2,  the  first  figure  on  the 
right  hand  of  the  one,  added  to  6,  the  first  figure  on 
the  right  hand  of  the  other,  makes  8,  which  is  therefore 
the  sum  of  these  two  parts.  Again,  the  sum  of  5 
and  3,  the  two  figures  or  parts  in  the  second  place,  is 
likewise  8.  But  now  as  figures  in  the  second  place, 
denote  not  simple  units,  but  tens  ;  hence  it  is  plain, 
that  5  and  3  here,  signify  five  tens  and  three  tens,  or 
50  and  30,  whose  sum  therefore  must  be  eight  tens  or 
80.  And  here  again,  I  call  to  mind,  that  having  al- 
ready obtained  one  figure  of  the  sum,  if  I  place  that 
now  found  immediately  after  it,  it  will  thereby  stand 
also  in  the  second  place,  and  so  really  express,  as  it 
ought  to  do,  eight  tens,  or  80.  And  thus  it  is  hap- 
pily contrived,  that  though  in  the  addition  of  the  tens, 
I  consider  the  figures  composing  them  as  denoting  on- 
ly simple  units,  which  makes  the  operation  easier  and 
less  perplexed  ;  yet  by  the  place  their  sum  obtains  in  the 
number  found,  it  expresses  the  real  amount  of  the  parts 


196  DUNCAN'S  ELEMENTS 

added,  taken  in  their  full  and  complete  values.  The 
same  thing  happens  in  summing  the  hundreds  and  thou- 
sands ;  that  is,  though  the  figures  expressing  these 
combinations,  are  added  together  as  simple  units  ;  yet 
their  sums,  standing  in  the  third  and  fourth  places  of 
the -number  found,  thereby  really  denote  the  hundreds 
and  thousands,  and  so  represent  the  true  value  of  the 
parts  added. 

Sec.   XII..*. Because  in  the  several  steps  by  which  it  is 
carried  on,  the  mind  is  put  to  liii-le  or  no  fatigue. 

Hence  then  we  have  a  manifest  proof  of  the  great 
advantages  derived  from  an  artful  method  of  classing 
our  perceptions.  For  as  the  numbers  themselves  are  by 
.this  means  distinguished  into  different  parts  which 
brings  them  more  readily  within  the  compass  of  the  un- 
derstanding ;  so  by  taking  these  parts  separately,  the 
operations  about  numbers  are  rendered  very  easy  and 
simple.  And  indeed  it  is  particularly  worthy  cur  no- 
tice, and  though  in  adding  two  very  large  numbers  to- 
gether, the  whole  process  is  of  sufficient  length  ;  yet 
the  several  steps  by  which  it  is  conducted,  are  managed 
with  incredible  dispatch,  and  scarce  any  fatigue  to  the 
jnind.  This  is  apparent  in  the  example  given  above, 
where  we  see,  that  in  every  advance  from  one  part  to 
another,  nothing  more  is  required  than  to  add  together 
the  two  figures  in  the  like  places  of  the  numbers  to  be 
summed.  But  what  is  yet  more  wonderful,  though  in 
the  progress  of  a  long  operation,  the  figures  rise  in  their 
value  as  we  advance,  and  grow  to  signify  thousands, 
millions,  billions,  4?V.  yet  so  happily  are  they  contriv- 
ed for  expressing  the  different  parts  of  numbers, 
that  in-  every  step  of  the  procedure  we  consider  them 
as  denoting  only  simple  units,  all  other  deficiencies  be- 
ing made  up,  by  the  places  their  sums  obtain  in  the  to- 
tal amount.  And  thus  it  is  so  ordered  in  this  admira- 
ble form  of  notation,  that  however  large  the  numbers 
are  that  come  under  examination,  they  are  neverthe- 
less managed  with  the  same  ease  as  the  most  simple 
and  obvious  collections ;  because  in  the  several  ope- 
rations about  .them,  the  mind  is  neither  tied  down  to 


OF  LOGIC.  197 

the  view  of  too  many  parts  at  once,  nor  entangled  with 
any  considerations  regarding  the  bulk  and  composition 
of  those  parts. 

Sec.  XIlI..:This  farther  Illustrated  by  an  Example  in 
Multiplication. 

And  if  these  advantages  are  so  very  manifest  in  the 
first  and  simplest  rules  of  arithmetic,  much  more  do  they 
discover  themselves  in  those  that  are  intricate  and  com- 
plex. Let  a  man  endeavour  in  his  thoughts  to  find 
the  product  of  two  numbers,  each  consisting  of  twen- 
ty or  thirty  places,  and  that  without  considering  the 
part3  separately  ;  I  believe  he  will  soon  be  sensible, 
that  it  is  a  discovery  far  beyond  the  limits  of  the  hu- 
man mind.  But  now  in  the  progressive  method  above  ex- 
plained, nothing  is  more  simple  and  easy.  For  if  we  take 
the  first  figure  on  the  right  hand  of  the  one  number, 
and  by  it  multiply  every  figure  of  the  other  separately  ; 
these  several  products,  connected  according  to  the  esta- 
blished laws  of  notation,  must  truly  represent  the  total 
product  of  this  other,  by  that  part  of  the  multiplying 
number.  Let  us  suppose,  for  instance,  the  figure  in 
the  unit's  place  of  the  multiplier  to  be  2,  and  the  three 
last  places  of  the  multiplicand  to  be  4.32.  Then,  2 
multiplying  2  produces  4,  which  therefore  is  the  first 
part  of  the  product.  Again,  2  multiplying  3  pro- 
duces 6.  But  now  3  standing  in  the  second  place  of 
the  multiplicand,  denotes  its  real  value  three  tens,  or 
30,  which  therefore  taken  twice,  amount  to  six  tensor 
60.  And  accordingly  the  figure  6,  coming  after  4  al- 
ready found,  is  thereby  thrown  into  the  second  place 
of  the  product,  and  so  truly  expresses  60,  its  full  and 
adequate  value.  The  same  thing  happens  in  multi- 
plying 4,  which  standing  in  the  place  of  hundreds,  its 
product  by  2  is  800.  But  this  very  sum  the  figure-8, 
produced  from  2  and  4,  really  denotes  ip  the  total  pro- 
duct. Because  coming  after  64,  the  two  parts  alrea- 
dy found,  it  is  thereby  determined  to  the  third  place, 
where  it  of  course  expresses  so  many  hundreds.  This 
process,  as  is  evident,  may  be  continued  to  any  length 
we  please  j  and  it  is  remarkable,  that  in  like  manner  as 
R  2 


198  DUNCAN'S  ELEMENTS 

in  addition,  though  the  value  of  the  figures  in  the  'mul- 
tiplicand continually  rises  upon  us,  yet  we  all  along 
proceed  with  them  as  simple  units ;  because  the  places 
©f  the  several  products  in  the  total  amountj  represent 
the  just  result  of  multiplying  the  figures  together,  ac- 
cording to  their  true  and  adequate  value. 

Sec.  XIV....Cy  the  disposition  of  the  several  Products 
in  order  to  Addition, 

Having  thus  obtained  the  product  by  the  first  figure 
of  the  multiplier,  we  next  take  that  in  the  second  place, 
and  proceed  with  it  in  the  same  manner.  This  second 
operation  gives  us  the  effect  of  that  figure,  consider- 
ed as  a  simple  digit.  But  as  it  stood  in  the  second 
place,  and  therefore  really  denoted  so  many  tens,  hence 
it  is  plain,  that  the  product  now  gained  must  be  yet 
multiplied  by  ten,  in  order  to  express  the  true  product 
sought.  This  is  accordingly  done  in  the  operation, 
by  placing  the  first  figure  of  this  second  product  under 
the  second  figure  of  the  first  product.  For  this,  when 
they  come  to  be  added  together,  has  the  same  effect 
as  annexing  a  cypher,  or  multiplying  by  ten,  as  every 
one  knows  who  is  in  the  least  acquainted  with  the  rules 
of  arithmetic.  In  like  manner,  when  we  multiply  by 
the  figure  in  the  third  place,  as  this  new  product  is 
placed  still  one  figure  backwards,  we  do  in  effect  an- 
nex two  cyphers  to  it,  or  multiply  it  by  a  hundred* 
And  this  we  ought  certainly  to  do  ;  because  having 
considered  the  multiplying  figure  as  denoting'  only  sim- 
ple units,  when  it  really  expressed  so  many  hundreds, 
the  first  operation  gives  no  more  than  the  hundreth 
part  of  the  true  product.  The  case  is  the  same  in 
multiplying  by  the  fourth  or  fifth  figures,  because,  the 
products  still  running  backwards,  we  thereby  in  effect 
annex  as  many  cyphers  to  them  as  bring  them  up  se- 
verally to  their  respective  adequate  value.  By  this 
means  it  happens,  that  though  the  figures  of  the  mul- 
tiplier in  every  advance,  denote  still  higher  and  higher 
combinations,  yet  we  all  along  proceed  with  them  as 
simple  digits  ;  the  disposition  of  the  several  products 
in  order  to  addition  making  up  for  all  the  deficiencits 


OF  LOGIC.  199 

that  arise  from  this  way  of  considering  them.  When 
in  this  method  of  procedure,  we  have  obtained  the  pro- 
duct of  the  multiplicand  into  all  the  different  parts 
of  the  multiplier,  by  adding  these  products  together  we 
obtain  also  the  total  product  of  the  two  numbers.  For 
since  the  whole  is  equal  to  all  its  parts,  nothing  is 
more  evident,  than  that  the  product  of  any  one  num- 
ber into  another,  must  be -equal  to  its  product  into  all 
the  parts  of  that  other  :  and  therefore  the  several  par- 
tial products  united  into  one  sum,  cannot  but  truly 
represent  the  real  product  sought. 

Sec.  XV. ..  ^Arithmetical  operations,  by  being  carried  on 
in  a  Progressive  method,  rendered  easy  and  intelligible. 

Thus  we  see,  that  in  questions  of  multiplication 
though  the  whole  process  is  sometimes  sufficiently  long 
and  tedious,  yet  the  several  steps  by  which  it  is  carried 
on  are  all  very  level  to  the  powers  of  the  understand- 
ing. For  from  the  account  given  above  it  appears,  that 
nothing  more  is  required  in  any  of  them  than  barely  to 
multiply  one  digit  by  another.  But  now  this  easy  rule 
of  operation  is  wholly  derived  from  the  before-menti- 
oned address#in  classing  our  perceptions.  For  to  this  it 
is  owing,  that  the  numbers  under  consideration  are  dis- 
tinguished into  parts,  and  that  the  several  parts  are  also 
clearly  represented  to  the  mind  in  the  very  form  of 
notation.  Now  as  these  parts  have  an  invariable  re- 
lation one  to  another,  and  advance  in  their  value  by 
an  uniform  law  of  progression  ;  the  understanding  by 
means  of  such  a  link  can  easily  hold  them  together, 
and  carry  its  views  from  stage  to  stage  without  per- 
plexity, or  confusion.  Hence  it  happens,  that  howe- 
ver large  and  mighty  the  numbers  are,  so  far  as  to  ex- 
ceed the  immediate  grasp  of  the  mind  ;  yet  by  run- 
ning gradually  through  the  several  combinations  of 
which  they  are  made  up,  we  at  length  comprehend 
them  in  their  full  extent.  And  because  it  would  be 
impossible  for  the  understanding  to  multiply  very  large 
numbers  one  into  another,  by  a  simple  effort  of  tho't ; 
therefore  here  also  it  considers  the  parts  separately, 
and,  taking  them  in  an  orderly  scries,   advances  by  a 


*200  DUNCAN'S  ELEMENTS 

variety  of  successive  steps.  It  is  true  indeed,  in  the 
progress  of  the  operation,  the  several  figures  rise  in  their, 
value  :  but  this  consideration  enters  not  the  work  it- 
self. For  there,  as  we  have  already  seen,  though  the 
characteis  are  taken  as  denoting  only  simple  units,  yet 
the  order  and  disposition  of  the  partial  products,  exhi- 
bits each  according  to  its  real  amount.  Hence  in  every 
step,  we  have  only  to  multiply  one  digit  by  another, 
which  as  it  is  attended  with  scarce  any  difficulty,  the 
whole  process  is  carried  on  with  wondrous  dispatch. 
And  thus  by  a  series  of  easy  operations,  we  at  length 
rise  to  discoveries,  which  in  any  other  method  of  pro- 
cedure, would  have  been  found  altogether  beyond  the 
reacn  of  the  mind. 

Sec.   XVI....  The   art  of  Classing  our  Perceptions  the 
great  Mean  and  Instrument  of  Invention. 

Since  therefore  by  a  due  and  orderly  disposition  of 
our  ideas,  we  can  brmg  the  most  wide  and  extended 
objects  upon  a  level  with  the  powers  of  the  understand- 
ing: and  since  by  this  also  we  abridge  the  fatigue  and 
labour  of  the  mind,  and  enable  it  to  carry  on  its  re- 
searches in  a  progressive  method,  without  which  con- 
trivance, almost  all  the  more  remote  and  distant  truths 
of  the  sciences  must  have  lain  for  ever  hid  from  our 
knowledge  ;  1  think  we  may  venture  to  affirm,  that  the 
art  of  regulating  and  classing  our  perceptions  is  the 
great  mean  and  instrument  of  invention-.  It  is  for  this 
reason  that  I  have  endeavoured  in  so  particular  a  man- 
ner to  illustrate  it  from  examples  in  numbers  ;  because 
we  have  here  not  only  a  perfect  model  of  the  art  itself, 
but  see  also  in  the  clearest  manner,  what  helps  it  fur- 
nishesV towards  a  ready  comprehension  of  objects,  and  a 
masterly  investigation  of  truth.  Nor  let  any  one  find 
fault,  as  if  we  had  insisted  rather  too  long  upon  matters 
that  are  obvious  and  known  to  all.  For  I  am  apt  to 
think,  that  though  very  few  are  strangers  to  the  re- 
ceived method  of  notation,  and  the  common  rules  of 
operation  in  arithmetic  ;  yet  it  is  not  every  one  that 
sets  himself  to  consider  the. address  and  sagacity  that 
Kiay  be  seen  in  the  contrivance  of  them,  or  to  unravel 


OF  LOGIC.  201 

those  principles  of  investigation,  which  we  have  here 
so  clearly  deduced  from  them.  And  this  I  take  to  be 
the  reason,  that  we  sometimes  meet  with  instances  of 
men,  who  though  thoroughly  versed  in  the  art  cf  in- 
vention ;  with  regard  to  some  particular  branches  of 
knowledge  ;  yet  if  taken  out  of  their  usual  track,  find 
themselves  immediately  at  a  stand,  as  if  wholly  bereft 
of  genius  and  penetration.  With  such  men  invention 
is  a  mere  habit,  carried  on  in  a  manner  purely  mecha- 
nical, without  any  knowledge  of  the  grounds  and  rea- 
sons upon  which  the  several  rules  of  investigation  art 
founded.  Hence  they  are  unfurnished  with  those  gene- 
ral observations,  which  may  be  alike  usefully  applied 
in  all  sciences,  with  only  some  little  necessary  varia- 
tions, suited  to  the  nature  of  the  subject  we '  are  upon. 
And  indeed  I  know  of  no  surer  way  to  arrive  at 
a  fruitful  and  ready  invention,  than  by  attending  care- 
fully to  the  procedure  of  our  own  minds,  in  the  exer- 
cise of  this  distinguished  faculty  ;  bexause  from  the 
particular  rules  relating  to  any  one  branch,  we  are 
often  enabled  to  derive  such  general  remarks,  as  tend 
to  lay  open  the  very  foundation  and  principles  of  the 
art  itself. 

Sec.    XVII....  The  manner  of  proceeding  in  the  resolu- 
tion of  Algebraic  questions. 

If  now  we  turn  our  thoughts  from  arithmetic  to  aU 
gebra,  here  also  we  shall  find,  that  the  great  invention 
lies,  in  so  regulating  and  disposing  our  notices  of 
things,  that  we  may  be  enabled  to  proceed  gradually  in 
the  search  of  truth.  For  it  is  the  principal  aim  of  this 
science,  by  exhibiting  the  several  relations  of  things  in  a 
kind  of  symbolical  language,  so  to  represent  them  to 
the  imagination,  as  that  we  may,  carry  our  attention 
from  one  to  another,  in  any  order  we  please.  Hence, 
however  numerous  those  relations  are,  yet  by  taking 
only  such  a  number  of  them  into  consideration  at  once, 
as  is  suited  to  the  reach  and  capacity  of  the  under- 
standing, we  avoid  perplexity  and  confusion  in  our  re- 
searches, and  never  put  our  faculties  too  much  upon 
the  stretch,  so  as  to  loose  ourselves  amidst  the  muUU 


202  DUNCAN'S  ELEMENTS 

plicity  of  onr  own  thoughts.  As  therefore  in  arithme- 
tic, we  rise  to  a  just  conception  of  the  greatest  num- 
bers as  considering  them  made  up  of  various  progres- 
sive combinations  ;  so  likewise  in  algebra,  those  mani- 
fold relations  that  often  intervene,  between  known 
and  unknown  quantities,  are  clearly  represented  to  the 
mind,  by  throwing^hem  into  a  series  of  distinct  equa- 
tions. And  as  the  most  difficult  questions  relating  to 
numbers  are  managed  with  ease  ;  because  we  can  take 
the  parts  air  figures  separately,  and  proceed  with  them 
one  after  another  ;  so  also  the  most  intricate  problems 
of  algebra  are  in  like  manner  readily  unfolded,  by  ex- 
amining the  several  equations  apart,  and  unravelling 
them  according  to  certain  established  rules  of  opera- 
tion. And  here  it  is  well  worth  our  notice,  that  in 
very  complicated  problems,  producing  a  great  number 
of  different  equations,  it  for  the  most  part  so  happens, 
that  every  one  of  them  includes  a  variety  of  unknown 
quantities.  When  therefore  we  come  to  solve  them 
separately,  as  it  would  too  much  distract  and  entangle 
the  mind,  to  engage  in  the  pursuit  of  so  many  differ- 
ent objects  at  once  ;  our  first  business  is,  by  artfully 
coupling  the  several  equations  together,  or  by  the  va- 
rious ways  of  multiplication,  subtraction,  addition,  and 
substitution,  to  derive  others  from  them  more  simple, 
until  at  length  by  such  a  gradual  process  we  arrive  at 
some  new  equation,  with  only  one  unknown  quantity. 
This  done,  we  set  ourselves  to  consider  the  equation 
last  found,  and  having  now  to  do  with  an  object  suit- 
ed to  the  strength  and  capacity  of  the  mind,  easily  by 
the  established  rules  of  the  art,  discover  the  quantity 
sought.  In  this  manner  we  proceed  with  all  the  se- 
veral unknown  quantities  one  after  another,  and  having 
by  a  series  of  distinct  operations  traced  them  separate- 
ly, the  question  is  thereby  completely  resolved. 

Sec.   XVIII....0/"  those  other  Artifices  which  may  be 
considered  as  Subsidiary  helps  to  Invention* 

,  Hence  it  appears,  that  the  business  of  invention,  as 
practised  in  algebra,  depends  entirely  upon  the  art  of 
abridging  our  thoughts,  reducing  the  number  of  par- 


OF  LOGIC  203 

ticulars  taken  under  consideration  at  once  to  the  few» 
est  possible,  and  establishing  that  progressive  method 
of  investigation,  which  we  have  already  so  fully  ex- 
plained from  examples  in  arithmetic.  I  might  easily 
show  that  the  same  observation  holds  equally  in  other 
sciences  ;  but  having  already  exceeded  the  bounds  I 
at  first  prescribed  to  myself  in  this  chapter,  shall  only 
add,  that  besides  the  grand  instruments  of  knowledge 
already  mentioned,  there  are  innumerable  other  artifi- 
ces, arising  out  of  the  particular  nature  of  the  subject 
we  are  upon,  and  which  may  be  considered  as  subsidi- 
ary helps  to  invention.  Thus  in  geometry,  many  de- 
monstrations of  problems  and  theorems  are  wholly  de- 
rived from  the  construction  of  the  figure  made  use  of, 
and  the  drawing  of  lines  from  one  point  to  another. 
In  like  manner  in  algebra,  the  devising  of  proper  equa- 
tions from  the  conditions  of  the  question  proposed,  and 
contriving  neat  expressions  for  the  unknown  quanti- 
ties, contribute  not  a  little  to  t|ie  easy  solution  of  pro- 
blems. And  when  we  have  even  carried  on  the  inves- 
tigation to  some  single  equation  with  only  one  unknown 
quantity  ;  as  that  unknown  quantity  may  be  various- 
ly perplexed  and  entangled  with  others-that  are  known, 
so  as  to  require  a  multiplicity  of  diiferent  operations, 
before  it  can  be  disengaged,  which  often  involves  us  in 
long  and  intricate  calculations,  and  brings  surds  and 
irrational  quantities  in  our  way  ;  algebraists,  to  pre- 
vent in  some  measure  these  inconveniences,  and  short- 
en as  much  as  possible  the  process,  have  fallen  upon 
several  methods  of  substitution,  which  are  of  great  ser- 
vice in  very  complicated  questions.  But  these  and  such 
like  artifices  of  invention,  cannot  be  explained  at 
length  in  this  short  essay.  It  is  enough  to  have  given 
the  reader  a  hint  of  them,  and  put  him  in  the  way  of 
unravelling  them  himself,  when  he  comes  to  apply  his 
thoughts  to  those  particular  branches  of  knowledge 
where  they  are  severally  made  use  of. 

Sec.   XIX. »*0f  the  great  advantages  arising   from   a 
happy  Notation  or  expression  of  our  Thoughts, 

There  is  one  thing  however,  that   in  a  particular 


204  DUNCAN'S  ELEMENTS 

manner  deserves  to  be  taken  notice  of,  before  we  dismiss 
this  subject  ;  and  that  is  the  great  advantages  that 
may  redound  to  science,  by  a  happy  notation  or 
expression  of  our  thoughts.  It  is  owing  entirely  to 
this,  and  the  method  of  denoting  the  several  combina- 
tions of  numbers  by  figures  standing  in  different  places, 
that  the  most  complicated  operations  in  arithmetic  are 
managed  with  so  much  ease  and  dispatch.  Nor  is  it  lesj 
apparent,  that  the  discoveries  made  by  algebra,  are 
wholly  to  be  imputed  to  that  symbolical  language  made 
use  of  in  it.  For  by  this  means  we  are  enabled  to  repre- 
sent the  relations  of  things  in  the  form  of  equations, 
and  by  variously  proceeding  with  these  equations,  to 
trace  out  tsep  by  step  the  several  particulars  we  are  in 
qmest  of.  Add  to  all  this,  that  by  such  a  notation,  the 
eyes  and  imagination  are  also  made  subservient  to  the 
discovery^  of  truth.  For  the  thoughts  of  the  mind  rise 
up, and  disappear,  according  as  we  set  ourselves  to  call 
them  into  view  ;  and  therefore,  without  any  particular 
method  of  fixing  and  ascertaining  them  as  they  occur, 
the  retrieving  them  again  when  out  of  sight,  would  of- 
ten be  no  less  painful  than  the  very  first*  exeieise  of  de- 
ducing them  one  from  another.  When  therefore  in 
the  pursuit  of  truth  we  carry  our  attention  forward 
from  one  part  of  the  investigation  to  another,  as  ne- 
vertheless we  have  frequent  occasion  to  look  back  upon 
the  discoveries  already  passed  through,  could  these  be 
no  otherwise  brought  into  view,  than  by  the  same 
course  of  thinking  in  which  they  were  first  traced,  so 
many  different  attentions  at  once  must  needs  greatly 
distract  the  mind,  and  be  attended  with  infinite  trdu- 
ble  and  fatigue.  But  now,  the  method  of  fixing  and 
ascertaining  our  thoughts  by  a  happy  and  well-chosen 
notation,  entirely  removes  all  these  obstacles.  For 
thus,  when  we  have  occasion  to  run  to  any  former  dis- 
coveries, as  care  is  taken  all  along  to  delineate  them 
in  proper  characters,  we  need  only  cast  our  eye  upon 
that  part  of  the  process  where  they  stand  expressed, 
which  will  lay  them  at  once  open  to  the  mind,  in  their 
true  and  genuine  form.  By  this  means  we  can  at  any 
time  take  a  quick  and  ready  survey  of  our  progress,  and 


OF  LOGIC.  205 

running  over  the  several  conclusions  already  gained, 
aee  more  distinctly  what  helps  they  furnish  towards  the 
obtaining  of  those  others  we  are  still  in  pursuit  cf. 
Nay  further,  as  the  amount  of  every  step  of  the  inves- 
tigation lies  fairly  before  us,  by  comparing  them  vari- 
ously among  themselves,  and  adjusting  them  one  to 
another,  we  come  at  length  to  discern  the  result  of  the 
whole,  and  are  enabled  to  form  our  several  discoveries 
into  an  uniform  and  well-connected  system  of  truths, 
which  is  the  great  end  and  aim  of  all  our  enquiries. 

Sec.   XX.... Recapitulation* 

Upon   the    whole  then  it  appears,  that  in  order  to 
proceed  succesfully  in  the  exercise  of    invention,    we 
must  endeavour  as  much  as  possible  to  enlarge  the  ca- 
pacity of  the  mind,  by  accustoming  it  to  wide  and  com- 
prehensive views  of  things  :   that   we    mull  habituate 
ourselves  to  a   strong  and  unshaken  attention,  which 
carefully  distinguishes  all  the  circumstances  that  come 
in  our  way,  and  lets  nothing  material  slip  its  notice  : 
in  fine,  that  we  must  furnish  ourselves   with  an  ample 
variety  of  intermediate  ideas,  and  be  much  in  the  exer- 
cise of  singling  them  out  and  applying  them  for  the 
discovery    of  truth.      These  preparatory  qualifications 
obtained,  what  depends  upon  art   lies    chiefly  in   the 
manner    of   combining  our  perceptions,  and  classing 
them  together  with  address,  so  as  to  establish  a  pro- 
gressive method  of  investigation.      And  here  it  is  cf 
great  importance  to  contrive  a  proper  notation  or  ex- 
pression of  our  thoughts,  such  as  may  exhibit  them  ac- 
cording to  their  real  appearance  in  the  mind,  and  dis- 
tinctly  represent    their  several  divisions,  classes,  and 
relations.     This  is  clearly  seen  in  the  manner  of  com- 
puting by  figures  in  arithmetic,  but  more  particularly 
in  that  symbolical  language,  which  hath  been  hitherto 
so    successively  applied  in  unravelling  of  algebraical 
problems.      j^hus   furnished,    we  may   at  any  time  set 
about  the  investigation  of  truth  ;  and  if  we  take  care 
to  note  down  the  several  steps  of  the  process,  as  the 
mind  advances  from  one  discovery  to  another,  such  an 
arrangement  or  disposition  of  our  thoughts  constitutes 
S 


206  DUNCAN'S  ELEMENTS 

what  is  called  the  method  of  invention.  For  thus  it  is 
plain  that  we  follow  the  natural  procedure  of  the  under- 
standing, and  make  the  truths  we  have  unravelled  to 
succeed  one  another,  according  to  the  order  in  which 
they  present  themselves  to  the  mind,  while  employed 
in  tracing  and  finding  them  out.  And  here  again  it  well 
deserves  our  notice,  that  as  by  this  means  the  whole  in- 
vestigation lies  distinctly  before  us ;  so  by  comparing' 
the  several  steps  of  it  among  themselves,  and  observing 
the  relation  they  bear  one  to  another,  we  are  enabled 
to  form  our  discoveries  into  a  regular  system  of  know- 
ledge, where  the  truths  advanced  are  duly  linked  toge- 
ther, and  deduced  in  an  orderly  series  from  first  princi- 
ples. This  other  manner  of  combining  our  thoughts, 
is  distinguished  by  the  name  of  the  method  of  science^ 
which  therefore  now  offers  itself  to  be  explained,  and 
is  accordingly  the  subject  of  the  ensuing  chapter. 


Cfcap.  II. 

OF  THE  METHOD  OF  SCIENCE. 

Sec.  I:. .Knowledge  as  derived  from  the  contemplation 
of  our  ideas j  of  a  necessary  and  unchangeable  nature  ; 

IN  order  to  give  the  juster  idea  of  the  rules  peculiar 
to  this  species  of  method,  and  establish  them  upon 
their  proper  foundation,  it  will  be  necessary  to  begin 
with  settling  the  meaning  of  the  word  science,  and 
showing  to  what  parts  of  human  knowledge  that  term 
may  be  most  fitly  applied.  We  have  already  observed, 
in  the  first  chapter  of  the  second  book,  that  there  are 
three  several  ways  of  coming  at  the  knowledge  of 
truih.  First,  by  contemplating  the  ideas  in  our  own 
minds.  Secondly,  by  the  information  of  the  senses. 
Thirdly,  by  the  testimony  of  others.  When  we  set 
ourselves  to  consider  the  ideas  in  our  own  minds,  we 
variously  compare  them  together,  in  order  to  judge  of 
their  agreement  or  disagreement.  Now  as  all  the  truths 
deduced  in  this  way,  flow  from  certain  connexions  and 
relations,  discerned  between  the  ideas  themselves  ;  and 


OF  LOGIC.  207 

a?  when  the  same  ideas  are  brought  into  comparison, 
the  same  relations  must  tver  and  Unvanbly  subsist 
between  them  ;  hence  it  is  plain,  that  the  knowledge 
acquired  by  the  contemplation  of  our  ideas,  is  of  a  ne- 
cessary and  unchangeable  nature.  But  farther,  as 
these  relations  between  our  ideas,  are  not  only  supposed 
to  be  real  in  themselves,  but  also  to  be  seen  and  dis- 
cerned by  the  mind  ;  and  as  when  we  clearly  perceive 
a  connexion  or  repugnance  betweeen  any  two  ideas,  we 
cannot  avoid  judging  them  to  agree  or  disagree  accord- 
ingly ;  it  evidently  follows,  that  our  knowledge  of  this 
kind  is  attended  with  absolute  certainty  and  conviction, 
insomuch,  that  it  is  impossible  for  us  to  withhold  our 
assent,  or  entertain  any  doubt  as  to  the  reality  of  truths 
so  offered  to  the  understanding.  .  The  relation  of  equa- 
lity between  the  whole  and  all  its  parts,  is  apparent  to 
every  one  who  has  formed  to  himself  a  distinct  notion 
of  what  the  words  whole  and  part  stand  for.  No  man, 
therefore,  who  has  these  two  ideas  in  his  mind,  can 
possibly  doubt  of  the  truth  of  this  proposition,  that  the 
ivholc  is  equal  to  all  its  parts.  For  this  would  be  only 
endeavouring  to  persuade  himself,  that  that  was  not, 
which  he  plainly  and  unavoidably  perceives  to  be.  So 
that  in  all  cases,  where  we  discern  a  relation  between 
any  of  our  ideas,  whether  immediately  by  comparing 
the  one  with  another,  or  by  means  of  intermediate 
ideas,  that  lay  it  open  distinctly  to  the  understanding  ; 
the  knowledge  thence  arising  is  certain  and  infallible. 
3  say  infallible  ;  because  we  not  only  perceive  and  own 
the  truth  of  propositions  so  offered  to  the  mind,  but, 
having  at  the  same  time  a,clear  view  of  the  ground  on 
which  our  assent  rests, are  entirely  satisfied  within  our- 
selves, that  we  cannot  possibly  be  deceived  in  this  per- 
ception. 

Sec.  J  I....  As  flowing  from  the  information  of  the  senses, 
begets  undoubted  assurance,  but  excludes  not  all  possi- 
bility of  being  deceived  ; 

.  This  second  way  of  coming  at  knowledge,  is  by  the 
means  of  the  senses.  From  them  we  receive  informati- 
on of  the  existence  of  objects  without  us,  of  the  unioia 


208  DUNCAN'S  ELEMENTS 

and  conjunction  of  different  qualities  in  the  same  sub- 
ject, and  of  the  operations  of  bodies  one  upon  another. 
Thus  our  eyes  tell  us,  that  there  is  in  the  universe  such 
a  body  as  we  call  the  sun,  our  sight  and  touch,  that 
light  and  heat,  or  at  least  the  power  of  exciting  those 
perceptions  in  us,  co-exist  in  that  body  ;  and  lastly,  by 
the  same  sight  we  also  learn,  that  fire  has  the  power 
of  dissolving  metals,  or  of  reducing  wood  to  charcoal 
and  ashes.  But  now  with  regard  to  this  kind  of  know- 
ledge we  are  to  observe,  that  though  when  the  organs 
of  the  body  are  rightly  disposed  and  operate  in  a  na- 
tu^gl  way,  we  never  doubt  the  testimony  of  our  senses, 
but  from  most  of  the  schemes  of  life  upon  their  infor- 
mation :  yet  are  not  the  truths  of  this  class  attended 
with  that  ahsolute  and  infallible  assurance,  which  be- 
longs to  those  derived  from  the  contemplation  of  our 
own  ideas.  We  fiad  that  the  senses  frequently  represent 
objects  as  really  existing,  which  yet  have  no  being  but 
in  our  own  imaginations  ;  as  in  dreams,,  phrensies, 
and  the  deliriums  of  a  fever.  A  disorder  too  in  the 
organs,  makes  us  often  ascribe  qualities  to  bodies,  en- 
tirely different  from  those  they  appear  to  possess  at 
other  times.  Thus  a  man  in  the  jaundice  shall  fancy 
every  object  presented  to  him  yellow  ;  and  in  bodily- 
distempers,  where  the  taste  is  greatly  vitiated,  what 
naturally  produces  the  idea  of  sweetness,  is  sometimes 
attended  with  a  Gju>te  contrary  sensation.  It  is  true, 
these  irregularities  neither  ought,  our  indeed  do  they, 
with  considerate  men,  in  any  ways  tend,  to  discredit 
the  testimony  of  experience.  Ke  that,  awake,  in  his 
senses,  and  satisfied  that  hjs  organs  operated  duly, 
should  take  it  into  his  head  tcy  doubt  whether  fire 
would  burn,  or  arsenic  poison  him,  and  therefore 
rashly  venture  upon  these  objects,  would  soon  be 
convinced  of  his  error,  in  a  way  not  much  to  his  liking*. 
As  nevertheless  the  senses  do  sometimes  impose  upon  us 
there  is  no  absolute  and  infallible  security  that  they 
may  not  at  others  ;  therefore  the  assurance  they  pro- 
duce, though  reasonable,  satisfying,  and  sufficiently 
well  founded  to  determine  us  in  the  several  actions 
and  occurences  of  life,  is  yet  of  such  a  nature,  as  not 


OF  LOGIC.  209 

necessarily  to  exclude  all  possibility  of  being  deceived 
Hence  some  men  go  so  far  as  to  maintain,  that  we  ought 
to  distrust  our  senses  altogether;  nay,  whole  sects  among 
the  ancients,  because  of  this  bare  possibility,  which  really 
extends  no  farther  than  to  matters  of  experience  and 
testimony,  yet  established  it  as  a  principle,  that  we  ought 
to  doubt  of  every  thing.  Nor  are  there  wanting  philo- 
sophers among  the  moderns,  who,  upon  the  same 
grounds,  deny  the  existence  of  bodies,  and  ascribe  the 
perceptions  excited  in  us,  not  to  the  action  of  external 
matter,  but  to  certain  established  laws  In  nature,  which 
operate  upon  us  in  such  manner  as  toproduce  all  thqise 
several  effects  that  seem  to  How  from  the  real^  presence 
of  objects  variously  effecting  our  perception.  It  is  not 
my  design  here  to  enter  into  a  particular  discussion  of 
these  matters  :  all  I  aim  at,  is  to  show,  that  the  testi- 
mony of  the  senses,  though  sufficient  to  convince  sober 
and  reasonable  men,  yet  does  not  sb  unavoidably  ex'iort 
our  assent,  as  to  leave  no  room  for  suspicion  or  dis- 
trust. 

Sec.  Ill ....  As  founded  upon  testimony,  is  of  a  still  ma 
certain  nature,'  though  in  many  cases  embraced wit fl- 
out wavering  or  disirust. 

The  third  and  last  way  of  coming  at  truth  is  by  the 
report  and  testimony  of  others.  This  regards  cmeriy 
past  facts  and  transactions,  which,  having  no  longer" 
any  existence,  cannot  be  brought  within  the  present 
sphere  of  our  observation.  For  as  these  could  never 
have  fallen  under  our  cognizance,  but  by  the  relations 
of  such  as  had  sufficient  opportunities  ot  being  inform- 
ed ;  it  is  hence  apparent,  that  all  our  knowledge  of 
this  kind  is  wholly  founded  upon  the  conveyance  of 
testimony.  But  now,  although  this  in  many  cases  is  a 
sufficient  ground  of  assent,  so  as  to  produce  a  ready  be- 
lief in  the  mind,  yet  is  it  liable  to  still  greater  objec- 
tions than  even  the  reports  ui  experience.  Ouj  sensesyj 
it  is  true,  on  some  occasions  aecefye  us.  and  therefore 
they  may  possibly  on  others.  But  this  bare  possibility 
creates  little  or  no  distrus.t^  because  there  are  u: 
rules  of  judging,  when  they  operate  according  to  na- 
S  2 


2!0  DUNCAN'S  ELEMENTS 

» 

ture,  and  when  they  are  prevented  or  given  up  to  ca- 
price. It  is  otherwise  in  matters  of  mere  human  testi- 
mony. For  there,  besides  the  supposition  that  the  per- 
sons  themselves  may  have  been  deceived,  there  is  a 
farther  possibility,  that  they  may  have  conspired  to 
impose  upon  others  by  a  false  relation.  This  considera- 
tion has  the  greater  weight,  as  we  frequently  meet 
with  such  instances  of  disingenuity  among  men,  and 
know  it  to  be  their  interest  in  some  particular  cases,  to 
dissemble  and  misrepresent  the  truth.  It  would,  never- 
theless, be  the  height  of  folly,  to  reject  all  human  tes-^ 
timony  without  distinction  because  of  this  bare  possi- 
bility. Who  can  doubt  whether  there  ever  were  in  the 
world  such  conquerors  as  Alexander  and  Julius  Cesar  ? 
There  is  no  absolute  contradiction,  indeed,  in  suppo- 
sing, that  historians  may  have  conspired  to  deceive  us. 
But  such  an  universal  concurrence  to  a  falsehood,  with- 
out one  contradicting  voice,  is  so  extremely  improba- 
ble, and  so  very  unlike  what  usually  happens  in  the 
world,  that  a  wise  man  could  as  soon  persuade  himself 
to  believe  the  grossest  absurdity,  as  to  admit  of  a  sup- 
position so  remote  from  every  appearance  of  truth. 
Kence  the  facts  of  history,  When  well  attested,  are 
yeadily  embraced  by  the  mind  ;  and  though  the  evidence 
attending  them  be  not  such  as  produces  a  neeessary  and 
infallible  assurance,  it  is  yet  abundantly  sufficient  to 
justify  our  belief,  and  leave  those  without  excuse,  who 
upon  the  bare  ground  of  possibility,  are  for  rejecting 
entirely  the  conveyance  of  testimony. 

Sec.  IV ....Science  belongs  entirely  to  that  branch  of know- 
ledge which  is  derived  from  the  contemplation  of  our 
Ideas. 

Upon  the  whole,  then,  it  appears,  that  absolute 
certainty,  such  as  is  attended  with  unavoidable  assent, 
and  excludes  all  possibility  of  being  deceived,  is  to  be 
found  only  in  the  contemplation  of  our  own  ideas.  In 
matters  of  experience  and  testimony,  men,  we  see, 
may  frame  pretences  for  suspicion  and  distrust  :  but  in 
that  part  of  knowledge  which  regards  the  relations  of 
tur  icteas,  none  such  can  have  place.     Tor  as  all  these 


OF  LOGIC.  211 

several  relations  are  either  immediately  discerned  by 
the  mind,  or  traced  by  means  of  immediate  ideas, 
where  self-evidence  is  supposed  to  accompany  every 
step  of  the  procedure,  it  is  absolutely  impossible  for  a 
man  to  persuade  himself  that  that  is  not,  which  he 
plainly  and  necessarily  perceives  to  be.  Now  it  is  to 
knowledge,  attended  with  this  last  kind  of  evidence 
alone,  that  in  strictness  and  propriety  of  speech  we  at- 
tribute the  name  of  science.  For  science  implies  per- 
ception and  discernment,  what  we  ourselves  see  and 
cannot  avoid  seeing  ;  and  therefore  has  place  only  in 
matters  of  absolute  certainty,  where  the  truths  ad- 
vanced are  either  intuitive  propositions,  or  deduced 
from  them  in  a  way  of  strict  demonstration.  And  as 
this  kind  of  certainty  is  no  where  to  be  found,  but  in 
investigating  the  relations  of  our  ideas  ;  hence  it  is 
plain,  that  science,  properly  speaking,  regards  wholly 
the  first  branch  of  human  knowledge  ;  that  which  we 
have  said  is  derived  from  a  contemplation  of  the  ideas 
in  our  own  minds. 

Sec.  V ... .Our  Knowledge  of  the  real  Existence  of  Ob- 
jects not  Intuitive, 

But  here  I  expect  it  will  be  asked,  if  science  and  de- 
monstration belong  only  to  the  consideration  of  our 
own  ideas,  what  kind  of  knowledge  it  is,  that  we  have 
relating  to  bodies,  their  powers,  properties,  and  opera- 
tions one  upon  another  ?  To  this  I  answer,  that  we 
have  already  distinguished  it  by  the  name  of  natural 
or  experimental.  But  that  we  may  see  more  distinctly 
wherein  the  difference  between  scientifical  and  natural 
knowledge  lies,  it  may  not  be  improper  to  add  the  fol- 
lowing observations.  When  we  cast  our  eyes  towards 
the  sun,  we  immediately  conclude,  that  there  exists  an 
object  without  us,  corresponding  to  the  idea  in  our 
minds.  We  are,  however,  to  take  notice,  that  this  con- 
clusion does  not  arise  from  any  necessary  and  unavoid- 
able connexion  discerned.,  between  the  appearance  of 
the  idea  in  the  mind,  and  the  real  existence  of  the  ob- 
ject without  us.  We  all  know  by  experience,  that  ideas 
jn,ay  be  excited,  and  that  too  by  a  seeming  operation 


212  DUNCAN'S  ELEMENTS 

of  objects  upon  our  senses,  when  there  are  in  fact  no 
such  objects  existing  ;  as  in  dreams,  and  the  deliriums 
of  a  feser.  Upon  what  then  is  the  before-mentioned 
conclusion  properly  grounded  ?  Why,  evidently  upon 
this  :  that  as  we  are  satisfied  our  organs  operate  duly, 
and  know  that  every  effect  must  have  a  cause,  nothing 
is  more  natural  than  to  suppose,  that  where  an  idea  is 
excited  in  the  mind,  some  object  exists  corresponding 
to  the  idea,  which  is  the  cause  of  that  appearance.  But 
as  this  conclusion,  by  what  we  have,  seen,  is  not  neces- 
sary and  unavoidable,  hence  there  is  no  intuition  in  the 
case,  but  merely  a  probable  conjecture,  or  reasonable 
presumption,  grounded  upon  an  intuitive  truth. 

Sec.  "VI..,. Absolute    Certainty    in   natural  Knowledge 
confined  to  %v hat  falls  under  our  immediate  notice* 

Again,  when  a  piece  of  gold  is  dissolved  in  aqua  re- 
gia,  we  see  indeed  and  own  the  effect  produced,  but  can- 
not be  said,  in  strictness  and  propriety  of  speech,  to 
have  any  perception  or  discernment  of  it.  The  reason 
is,  because  being  unacquainted  with  the  intimate  :  ia- 
ture  both  of  aqua  regia  and  gold,  we  cannot,  from  the 
ideas  of  them  in  our  minds,  deduce  why  the  one 
operates  upon  the  other  in  that  particular  manner. 
Hence  it  is,  that  our  knowledge  of  the  facts  and  opera- 
tions of  nature  extends  not  with  certainty  beyond  the 
present  instance,  or  what  falls  under  our  immediate 
notice  ;  so  that  in  all  our  researches  relating  to  them, 
we  must  proceed  ijn  the  way  of  trial  and  experiment, 
there  being  here  no  general  or  universal  truths,  v  here- 
on to  found  scientijical  deductions.  Because  the  solu- 
tion of  gold  in  aqua  regia  holds  in  one  experiment, 
we  cannot  thence  infallibly  conclude  that  it  will  "hold 
in  another.  For  not  knowing  upon  what  it  is,  in  either 
of  these  bodies,  that  the  effect  here  mentioned  depends 
we  have  no  absolute  certainty  in  any  new  experiment 
we  propose  to  make,  that  the  objects  to  be  applied  one 
to  another  have  that  precise  texture  and  constitution 
from  which  this  solution  results.  Che-mists  know  by 
experience,  that  bodies  which  go  by  the  same  name, 
and  have  the  game  outward  appearance,  are  not  always, 


OF  LOGIC.  213 

however,  exactly  alike  in  their  powers  and  operations. 
In  rain  do  they  often  search  for  those  properties  in 
one  piece  of  antimony,  which,  on  former  occasions,  - 
they  may  have  found  in  another  ;  and  hy  this  means, 
to  their  no  small  mortification,  find  themselves  fre- 
quently disappointed,  in  very  costly  and  promising  ex- 
periments. Nor  have  we  any  express  and  positive  as- 
surance, that  the  very  bodies  with  which  we  have  for- 
merly made  experiments, continue  so  exactly  the  same, 
as  to  afford  the  like  appearances  in  any  succeeding 
trial.  A  thousand  changes  happen  every  moment  in 
the  natural  world,  without  our  having  the  least  know- 
ledge or  perception  of  them.  An  alteration  in  our  at- 
mosphere, the  approach  or  recess  of  the  sun,  his  decli- 
nation towards  the  north  or  south,  not  only  vary  the 
outward  face  of  things,  but  occasion  many  changes  in 
the  human  constitution  itself,  which  we  yet  perceive 
not  when  they  happen  ;  nor  should  ever  be  sensible  of, 
but  by  the  effects  and  consequences  resulting  from 
them.  And  whether  alterations  analogous  to  these 
Jhay  not  sometimes  be  produced  in  the  frame  and  tex- 
ture of  many  bodies  that  surround  us,  is  what  we  can- 
not with  certainty  determine.  Hence,  from  an  expe- 
riment's succeeding  in  one  instance,  Ave  cannot  infal- 
libly argue,  that  it  will  succeed  in  another,  even  with 
the  same  body.  The  thing  may  indeed  be  probable, 
and  that  in  the  highest  degree  ;  but  as  there  is  still  a 
possibility  that  some  change  may  have  happened  to  the 
body,  unknown  to  us?  there  can  be  no  absolute  cer- 
tainty in  the  case. 

Sec.    VII....  What   kind  of  Knowledge  of  Body  would 
deserve  the  name  cf  Science, 

Had  we  such  an  intimate  acquaintance  with  the 
structure  both  of  aqua  regie  and  gold,  as  to  be  able 
thence  to  discern  why  the  one  so  operates  upon  the 
other  as  to  occasion  its  dissolution  ;  insomuch  that 
from  the  ideas  of  them  in  our  own  minds,  we  could 
clearly  deduce,  that  bodies  of  such  a  make  applied  one 
to  another,  must  necessarily  produce  the  effect  here 
mentioned  j  our  knowledge  would  then  be  scientifcal. 


214  DUNCAN'S  ELEMENTS 

and  stand  upon  the  foundation  cither  of  intuition  or 
demonstration^  according  as  the  perception  was  imme- 
diate, or  attained  by  means  of  intervening  ideas.  In 
this  case,  therefore,  having  two  standard  ideas  in  our 
minds,  whose  relations  we.  perfectly  well  know;  wher- 
ever we  found  objects  conformable  to  these  ideas,  we 
could  then  pronounce  with  certainty,  that  the  applica- 
tion of  them  one  to  another  would  be  attended  with  the 
above  effect :  because,  whatever  is  true  in  idea,  is  un- 
avoidably so  also  in  reality  of  things,,  where  things 
exist  answerable  to  these  ideas.  If  it  be  true  in  idea, 
that  a  parellelogram  is  the  double  of  a  triangle,  stand- 
ing upon  the  same  base,  and  between  the  same  parel- 
lels  ;  the  same  will  be  true  of  every  real  triangle  and 
parellelogr/un,  that  exist  with  the  conditions  here  men- 
tioned. We  are  likewise  to  observe,  that  the  changes 
to  which  bodies  are  daily  liable,  could  produce  no  con- 
fusion or  perplexity  in  natural  knowledge,  did  it  stand 
upon  the  foundation  here  mentioned.  For  in  such  a 
case,  the.powers  and  properties  of  objects  being  dedu- 
ced from  the  ideas  of  t\rmi  in  our  own  minds,  would 
no  otherwise  be  applied  to  things  really  existing,  than 
as  these  things  are  found  perfectly  conformable  to  our 
ideas.  When,  therefore,  an  alteration  happened  in 
any  body,  as  it  would  by  this  mean?  differ  from  that 
standard  idea  whence  its  former  properties  were  seen 
to  flow,  we  must  of  course  be  sensible,  that  some  suit- 
able change  would  follow  in  the  properties  themselves, 
and  that  its  powers  and  operations,  in  regard  of  other 
bodies,  would  not  be  in  all  repects  the  same. 

Sec»  VIII,... Experience  the  only  foundation  of  Natu- 
ral Knowledge. 

But  what  is  still  more  remarkable,  we  should,  upon 
this  supposition,  be  able  to  determine  the  mutual  ac- 
tion and  influence  of  bodies,  without  having  recourse 
to  trial  or  experiment.  Had  we,  for  instance,  a  perfect 
knowledge  of  the  intimate  nature  and  composition  of 
an  animal  body,  and  of  that  particular  poison  that  is 
infused  into  it  by  the  bite  ©f  a  viper,  so  as  clearly  and 
olistictly  to  discern  how  they  are  adapted    one    to  ano- 


OF  LOGIC.  215 

ther;  we  might  thence  scientifically   deduce,  without 
the    help    of  experiments,   that    the    bite   of  a    viper 
would  so  unhinge  the  human  fabric,  and  produce  such 
ferments  and  combustions  in  it,  as  must  necessarily  be 
followed  by  a  total  extinction  of  all  the  vital  functions, 
and  leave  that  admirable  machine  a  mere  lifeless  lump. 
But  as  such  perfect  and  adequate  ideas  of  objects,  and 
their  mutual  habitudes  one   to  another,  are  plainly  be- 
yond the  reach  of  our  present  faculties  ;  it  were  vain  for 
us  to  think  of  improving  natural  knowledge  by  abstract 
reasoning  or  stientifical  deductions.  Experience  is  here 
the  true  and  proper  foundation  of  our  judgments,  nor 
can  we  by  any  other  means  arrive  at  a  discovery  of  the 
several  powers  and  properties  of    bodies.      How    long 
might  a  man  contemplate  the  nature  of  hemlock,  exa- 
mine the  structure  of  its   parts   in  a  microscope,  and 
torture  and  analyse  it  by  all  the  processes  of  chemistry, 
before  he  could  pronounce  with  certainty  the  effect  it 
will  have  upon  a  human  body?   One  single  experiment 
lays  that  open  in  an  instant,  which  all  the   wit  and  in- 
vention ot  ixen  would  never  of    themselves  have  beer* 
able  to  trace.   The  same  holds  in  all  the  other  parts  of 
natural  philosophy.  Our  discoveries  relating  to.  electri- 
city, the  powers  and  properties  of  the  load-stone,  the 
force  of  gunpowder,  &c.  were  not  gained    by   reason- 
ing, or  the  consideration  of  our  abstract  ideas,  but   by 
means  of  experiments  made  with  the  bodies  themselves. 
Hence  it  happened,  that  while  the  philosophy  of  Aris- 
totle prevailed  in    the    schools,  which  dealt  much    in 
metaphysical  notions,  occult  qualities,  sympathies,  an- 
tipathies, and  such  like   words  without  meaning  ;   the 
knowledge  of  nature  was  at  a  ?tand  :   because  men  pre- 
tended to  argue  abstractedly  about  the  things  of  which 
they   had  no  perfect    and    adequate  ideas,    whereon  to 
ground  such  a    method  of   reasoning.     But  now  in  the 
present  age,  that  we  have  returned  to  the  way  of  trial 
and  experiment,  which  is  indeed  the  only  true  founda- 
tion of  natural   philosophy;  great   advances    have  al- 
ready been  made,  and  the  prospect  of  still  greater  lies 
before  us. 


216  DUNCAN'S  ELEMENTS 

Sec.    IX.,.. Difference  between  Scientifical  and  Natural 
Kn$w  ledge* 

And  thus  at  length  we  may  sufficiently  understand 
■wherein  the  proper  difference  lies,  between  scientifiai 
and  natural  knowledge.  In  matters  of  science  we  argue 
from  the  ideas  in  our  own  minds,  and  the  connexions 
and  relations  they  have  one  to  another.  And  as  when 
these  relations  are  set  clearly  and  plainly  before  us,  we 
cannot  avoid  peceiving  and  owning  them,  hence  all 
the  truths  of  this  class  produce  absolute  certainty  in  the 
mind,  and  are  attended  with  a  necessary  and  unavoid- 
able assent.  It  is  otherwise  in  the  case  of  natural  know- 
ledge. Intuition  and  inward  perception  have  here  no 
place.  We  discern  not  the  powers  and  properties  of 
those  objects  that  surround  us,  by  any  view  and  com- 
parison of  the  ideas  of  them  one  with  another,  but 
merely  by  experience,  and  the  impressions  they  make 
on  the  senses.  But  now  the  reports  of  sense  happening 
in  some  instances  to  deceive  us,  we  have  no  infallible 
assurance  that  they  may  not  in  others;  which  weakens 
not  a  little  the  evidence  attending  this  kind  of  know- 
ledge, and  leaves  room  for  suspicion  and  distrust.  Nay, 
what  is  yet  more  considerable,  as  we  have  no  perfect 
and  adequate  ideas  of  bodies,  representing  their  inward 
constitution,  or  laying  open  the  foundation  upon 
which  their  qualities  depend,  we  can  form  no  universal 
propositions  about  them,  applicable  with  certainty  in 
all  particular  instances.  Fire,  we  say,  dissolves  metals. 
This,  though  expressed  indefinitely,  is,  however,  only 
a  particularly  truth,  nor  can  be  extended  with  absolute 
assurance,  beyond  the  several  trials  made.  The  reason 
is,  that  being  ignorant  of  the  inward  frame  and  com- 
position both  of  fire  and  metals  ;  when  objects  are  offer- 
ed to  us  under  that  name,  we  have  therefore  no  posi- 
tive certainty  that  they  are  of  the  very  make  and  tex- 
ture, requisite  to  the  success  of  the  experiment.  The 
thing  may  indeed  be  probable  in  the  highest  degree  ; 
but  for  want  of  standard  and  settled  ideas,  we  can 
never  arrive  at  a  clear  and  absolute  perception  in  the 
case. 


OF  LOGIC.  217 

»5ec.  X....77j£  manner  of  Reasoning  in  Natural  Know* 
ledge* 
As  nevertheless,  it  is  certain  that  many  general  con» 
elusions  in  natural  philosophy  are  embraced  without 
doubt  or  hesitation ;  nay,  that  we  form  most  of  the 
schemes  and  pursuits  of  life  upon  that  foundation  ;  it 
will  naturally  be  asked  here,  how  come  we  by  this  assu- 
rance ?  I  answer,  not  scientifically,  and  in  the  way  of 
strict  demonstration,  but  by  analogy,  and  an  induction 
of  experiments.  We  distinguish  fire,  for  instance,  by 
such  of  its  qualities  as  lie  more  immediately  open  to  the 
notice  of  the  senses  ;  among  which  light  and  heat  are 
the  most  considerable.  Examining  still  farther  into  its 
nature,  we  find  it  likewise  possessed  of  the  power  of  dis- 
solving metals.  But  this  new  property  not  having  any 
necessary  connexion  that  we  can  trace,  with  those  other 
qualities  by  which  fire  is  distinguished,  we  cannot  there* 
fore  argue  with  certainty,  that  wherever  light  and  heat, 
&c.  are,  the  power  of  dissolving  metals  co-exists  with 
them.  'Tis  not  till  after  we  have  tried  the  thing  in  a 
variety  of  experiments,  and  found  it  always  to  hold, 
that  we  begin  to  presume  there  may  be  really  some 
such  connexion,  tho*  our  views  are  too  short  and  imper- 
fect to  discover  it.  Hence  we  are  led  to  frame  a  general 
conclusion,  arguing  from  what  has  already  happened, 
to  what  will  happen  again  in  the  like  cases  insomuch 
that  where  we  meet  with  all  the  other  properties  of  fire 
in  any  body,  we  have  not  the  least  doubt,  but  that  upon 
trial,  the  power  above-mentioned  will  be  found  to  be- 
long to  it  also.  This  is  called  reasoning  by  analogy; 
and  it  is,  as  we  see,  founded  entirely  upon  induction, 
and  experiments  made  f with  particular  objec  s  ;  the 
more  precise  and  accurate  our  ideas  of  these  objects  are, 
and  the  greater  the  variety  of  experiments  upon  which 
we  build  our  reasoning,  the  more  certain  and  undoubt- 
ed will  the  conclusions  be.  'Tis.in  this  manner  we  ar- 
rive at  all  the  general  truths  of  natural  knowledge  :  as 
that  the  bixe  of  a  certain  animal  is  mortal ;  that  a  needle 
touched  by  a  loadstone  points  to  the  north ;  that  gravi- 
ty belongs  universally  to  all  bodies;  and  innumerable 
others,  which,  though  not  capable  of  strict  demonstra- 
T 


218  DUNCAN'S  ELEMENTS 

tion,  are  nevertheless  as  readily  embraced  upon  the 
foundation  of  analogy,  as  the  most  obvious  and  intui- 
tive judgments  ;  nay,  and  become  fixed  and  steady  prin- 
ciples of  action,  in  all  the  aims  and  pursuits  of  life. 

Sec.  XI....//0W  even  Scientijical  Reasoning  maybe  in* 
troduced  into  it* 

And  here  again  it  is  particularly  remarkable,  that 
having  ascertained  the  general  properties  of  things  by 
analogy,  if  we  proceed  next  to  establish  these  as  postu* 
lata  in  philosophy,  we  can,  upon  this  foundation,  build 
strict  and  mathematical  demonstrations,  and  thereby 
introduce  scientijical  reasoning  into  natural  knowledge. 
In  this  manner,  six  Isaac  Newton  having  determined  the 
laws  of  gravity  by  a  variety  of  experiments,  and  laying 
it  down  as  a  principle,  that  it  operates  according  to 
those  laws  through  the  w7hole  system  of  nature  ;  has 
thence,  in  a  way  of  strict  demonstration,  deduced  the 
whole  theory  of  the  heavenly  motions.  For  granting 
once  this postulatum,  that  gravity  belongs  universally  to 
all  bodies,  and  that  it  acts  according  to  their  solid  con- 
tent, decreasing  with  the  distance  in  a  given  ratio  ; 
"what  sir  Isaac  has  determined  in  regard  to  the  planetary 
motions,  follows  from  the  bare  consideration  of  our 
own  ideas  ;  that  is,  necessarily  and  scientifically.  Thus 
likewise  in  optics,  if  we  lay  it  down  as  a  principle,  that 
light  is  propagated  on  all  sides  in  right  lines,  and  that 
the  rays  of  it  are  reflected  and  refracted  according  to 
certain  fixed  invariable  laws  all  which  is  known  to  be 
true  by  experience  ;  we  can  upon  this  foundation  esta- 
blish mathematically  the  theory  of  vision.  The  same 
happens  in  mechanics,hjdrostatics1pneamatics<ihc.whcY& 
from  postulata  ascertained  by  experience,  the  whole 
theory  relating  to  these  branches  of  knowledge  follow* 
in  a  way  of  strict  demonstration.  And  this  1  take  to  be 
the  reason  why  many  parts  of  natural  philosophy  arc 
konored  with  the  name  of  sciences*  Not  that  they  are 
ultimately  founded  upon  intuition  ;  but  that-the  several 
principles  peculiar  to  them  being  assumed  upon  the 
foundation  of  experience,  the  theory  deduced  from 
these  principles  is  established  by  scientijical  reasoning'. 


OF  LOGIC.  21% 

Sec.  XII. ...Yet  still  Experience  is  the  ultimate  Ground 
of  our  Assent. 
Could  we  indeed  discern  any  necessary  connexion  be- 
tween gravity  and  the  known  essential  qualities  of  mat- 
ter, insomuch  that  it  was  inseparable  from  the  very  idea 
pf  it  ;  the  whole  theory  of  the  planetary  motions  would 
then  be  strictly  and  properly  scicntijiral^  For  seeing, 
from  the  notion  of  gravity,  we  can  demonstratively  de- 
termine the  laws  that  bodies  will  observe  in  their  revo- 
lutions, in  any  known  circumstances  ;  if  the  circum- 
stances relating  to  any  system  of  bodies  can  be  traced, 
and  gravity  is  supposedessential  to  them,  we  can  then, 
from  the  bare  consideration  of  our  own  ideas,  deduce 
all  their  motions  and  phenomena.  Now  this  is  precise- 
ly what  sir  Isaac  has  done  in  regard  to  our  planetary 
system.  Hs  has  determined  the  circumstances  of  the 
bodies  that  compose  it,  in  respect  of  situation,  distance, 
magnitude,  See.  all  which  being  supposed,  if  they  are 
essentially  actuated  by  gravity,  their  several  revolutions 
and  appearances  must  be  equally  essential.  But  as  the 
principle  of  gravitation  cannot  be  accounted  for  by  the 
known  qualities  of  matter,  neither  can  this  theory  be 
immediately  deduced  from  the  idea  of  body  ;  and  there- 
fore, tho'  our  reasoning  in  this  pr.rt  of  philosophy  be 
truly  scienti£cal,  yet  as  the  principle  upon  which  that 
reasoning  is  grounded,  is  derived  from  experience,  the 
theory  itself  must  needs  ultimately  rest  upon  the  same 
foundation.  And  thus  even  the  doctrine  of  the  pla- 
netary motions,  though  seemingly  established  by  ma- 
thematical reasoning,  falls  yet,  in  strictness  and  pro- 
priety of  speech,  under  the  head  of  natural  knowledge. 
For  in  this  precisely  consists  the  difference  between 
science,  and  what  we  call  the  philosophy  of  nature ;  that 
the  one  is  grounded  ultimately  on  intuition,  the  other 
on  experience.  As  the  observation  here  made  holds  alike 
in  all  the  other  branches  of  natural  philosophy,  into 
•which  scientijical  reasoning  has  been  introduced;  it  is 
hence  apparent,  that  they  are  not  sciences,  in  the  strict 
and  proper  sense  of  the  word,  but  only  by  a  certain 
latitude  of  expression  common  enough  in  all  languages. 
What  we  have  therefore  said  above,  relating  to  theim- 


220  DUNCAN'S  ELEMENTS 

possibility  of  improving  natural  knowledge,  by  scienti- 
fical  deductions,  is  not  contradicted  by  any  thing  ad- 
vanced in  this  section.  We  there  meant  deductions 
grounded  ultimately  on.  intuition,  and  derived  from  a 
consideration  of  the  abstractideas  of  objects  in  our  own 
minds  ;  not  such  as  flow  from  postulata,  assumed  upon 
the  foundation  of  experience.  For  these  last,  as  we  have 
already  observed,  are  not  truly  and  properly  scientifi- 
cal,  but  have  obtained  that  name  merely  on  account  of 
the  way  of  reasoning  in  which  they  are  collected  from 
the  said  postulata. 

Sec.  XIII. ...77i£  manner  of  Reasoning   in  Historical 
Knowledge, 

If  then  absolute  and  infallible  certainty  is  not  to  be 
fcbtaiaed  in  natural  knowledge,  much  less  can,  we  ex- 
pect it  in  historical.  For  here  testimony  is  the  only 
ground  of  assent ;  and  therefore  the  possibility  of  our 
being  deceived,  is  still  greater  than  in  the  case  of  ex- 
perience. Not  only  he  who  reports  the  fact  may  himself 
have  formed  a  wrong  judgment;  but  could  we  even 
get  over  this  scruple,  there  is  still  room  to  suspect,  that 
be  may  aim  at  imposing  upon  us  by  a  false  narration. 
In  this  case,  therefore,  it  is  plain,  there  can  be  no  in- 
tuition or  inward  perception"  of  truth,  no  strict  and  ab- 
solute demonstration,  and  consequently  no  science. 
There  is,  however,  a  way  of  reasoning  even  here,  that 
begets  anentire  acquiescence,  and  leads  us  to  embrace 
without  wavering,  the  facts  and  reports  of  history.  If, 
for  instance,  it  appears,  that  the  historian  was  a  man 
of  veracity;  if  he  was  a  competent  judge  of  what  he 
relates  ;  if  he  had  sufficient  opportunities  of  being  in- 
formed; if  the  book  that  bears  his  name  was  really 
written  by  him  ;  if  it  had  been  handed  down  to  us 
uncorrupted  ;  in  fine,  if  what  he  relates  is  probable 
in  itself,  falls  in  naturally  with  the  other  events  of 
that  age,  and  is  attested  by  contemporary  writers: 
by  these  and  such  like  arguments,  founded  partly  on 
criticism,  partly  on  probable  conjecture,  we  judge  of 
past  transactions ;  and  though  they  are  not  capable  of 
scientiJicai^rooL  yet  in  many  cases  we  arrive  at  an  un- 


OF   LOGIC.  221 

doubted  assurance  of  them.  For  as  it  is  absurd  to  de- 
mand mathematical  demonstration  in  matters  of  fact, 
because  they  admit  not  of  that  kind  of  evidence  ;  it  is 
no  less  so  to  doubt  of  their  reality,  when  they  are  prov- 
ed by  the  best  arguments  their  nature  and  quality  will 
bear. 

Sec.  XIV. ...Scepticisms  necessarily  excluded  from  mat- 
ters of  Science  ; 

Ana"  thus  we  see,  in  the  several  divisions  of  human 
knowledge,  both  what  i3  the  ground  of  judging,  and 
the  manner  of  reasoning,  peculiar  to  each.    In  scientific 
cal  knowledge,  which  regards  wholly  the  abstract  ideas 
of  the  mind,  and  those  relations  and  connexions  they 
have  one  with  another ;  our  judgments   are   grounded 
on  intuition,  and  the  manner  of  reasoning  is  by  demon- 
stration.   In  natural  knowledge,  respecting  objects  that 
exist  without  us,  their  powers,  properties,,  and  mutual 
operations  ;   we  judge   on  the  foundation  of  experience 
and  reason  by  induct  ion  and  analogy.  Lastly,  in  historical 
xnowl edge,  \sh\z\\  is  chiefly  conversant  about  past  facts 
and  transactions,  testimony  is  the  ground  of  judgment, 
and  the  way  of  reasoning  is  by  criticism  and  probable 
conjecture.   And  now  I  think  we  are  able  effectually  to 
overthrow  that  absurd  kind  of  scepticism  maintained  by 
some  of  the  ancients  which  brings  all  propositions  up- 
on a  level,   and  represents  them   as  equally  uncertain. 
What  gave  the  first  rise  to  this  doctrine   was,  caprice 
of  certain  philosophers,  whoobserving  that  the  reports 
ot  sense  and  testimony  were  in  some  instances  deceitful, 
took  thence  occasion  to  suppose  that  they  might  be  so 
likewise  in  others,    and    thereupon  established  it  as  a 
principle,  that  we  ought  to  doubt  of  every  thing.      But 
even  with  repecf  to  this  doubting,  we  are  to  observe, 
that  it  can  in  fact  extend  no  farther,  than  to  matters  of 
experience  and  testimony,  being  totally  and  necessarily- 
excluded  from  scientifcal  knowledge.  When  ideas  make 
their  appearance  in  the  understanding,  it  is  impossible 
for  us  to  doubt  of  their  being  there.     And  when  the 
relations  of  any  of  our  ideas  are  clearly  and  distinctly 
discerned  by  the  mind,  either  immediately,  which  is 
T  2 


222  DUNCAN'S  ELEMENTS 

intuition,  or  by  means  of  intervening  ideas,  which  is 
demonstration  ;  itwould  be  in  vain  for  us  to  endeavour 
to  persuade  ourselves  that  that  is  not,  which  we  plain- 
ly, and  unavoidably  perceive  to  be.  In  this  case,  there- 
fore, we  cannot  withhold  our  assent ;  truth  forces  its 
way  over  all  opposition, and  breaks  in  with  so  much  light 
upon  the  mind,  as  to  beget  "absolute'  and  infallible  cer- 
tainty. 

Sec.  JLY„„Andto  be  admitted  with  caution  in  matters 
of  experience  and  testimony. 

Indeed  in  natural  and  historical  knowledge  scepticism 
may  have  place  ;  because,  as  we  have  said,  there  is  a  possi- 
bility of  our  being  deceived.  But  then  it  is  to  be  observed, 
that  a  bare  possibility  is  a  very  weak  ground  whereon 
to  bottom  any  philosophical  tenet.  It  is  possible,  that 
Great  Britain  may  be  swallowed  up  by  the  sea  before 
to-morrow;  but  1  believe  no  man  is  on  this  account  in- 
clined to  think  that  it  will  be  so.  It  is  possible,  the 
whole  human  race  may  be  extinguished  the  next  in- 
stant ;  yet  this  possibility  creates  no  apprehension  that 
the  thing  itself  will  really  happen.  In  a  word,  we  ought  to 
judge  of  things  by  the  proofs  brought  to  support  them, 
.not  by  bare  abstrast  possibilities  ;  and  when  we  have 
all  the  evidence,  they  are  capable  of,  that  alone  is  suf- 
ficient to  convince,  though  perhaps  the  contrary  cannot 
be  shown  to  imply  a'contradiction.  Will  any  wise  and 
considerate  man  doubt  whether  there  be  such  a  place 
as  Africa^  because  we  cannot  prove,  by  any  necessary 
argument,  that  it  is  absolutely  impossible  all  the  relati- 
ons concerning  it  should  be  false?  Strict  and  rigorous 
demonstrations  belong  not  to  history,  or  the  philoso- 
phy of  Nature.  The  way  of  reasoning,  in  these  bran- 
ches of  knowledge,  is  by  arguments  drawn  from  expe- 
rience and  testimony.  And  when  the  truth  of  any  pro- 
-  position  is  in  this  manner  sufficiently  ascertained,  inso- 
much that  it  appears  with  all  the  evidence  it  is  capable 
©f,  and  we  kave  as  great  reason  to  believe  that  it  is,  as 
we  could  possibly  have,  supposing  it  were,  is  not  this 
upon  the  matter  as  satisfactory  as  a  demonstration?  It 
must  be  owned,  indeed,  there  is  no  inward  perception 
1 


OF  LOGIC.  223 

in  the  case  ;  and  therefore  our  assent  cannot  be  said 
to  be  necessary  and  unavoidable.  Men  may  in  these 
matters  be  sceptics^  if  they  please  ;  and  if  they  are  re- 
solved upon  it,  it  is.  in  vain  to  contend  with  obstinacy 
and  pervcrseness.  I  cannot,  however,  but  observe,  that 
if  they  will  really  act  up  to  their  own  principles,  and 
treat  all  things  in  good  earnest  as  uncertain,  that  ad- 
mit not  of  strict  scientifical  proof, their  conduct  must 
be  the  very  madness  of  folly.  No  man  can  demonstrate 
mathematically,  that  poison  has  not  been  conveyed 
into  his  meat  or  drink.  And  if  he  will  be  so  very  cau- 
tious as  not  to  taste  of  either,  till  he  has  reached  this 
degree  of  certainty,  I  know  no  other  remedy  for  him, 
but  that  in  great  gravity  and  wisdom  he  must  die  for 
fear  of  death.  The  truth  of  it  is,  the  most  zealous 
patrons  ot  scepticism^  after  all  their  pretended  doubts 
and  scruples  find  it  yet  convenient  to  behave,  in  the  se- 
veral occurrences  of  life,  as  if  they  gave  entire  credit  to 
the  reports  of  sense  and  testimony.  They  will  no  more 
venture  upon  a  dose  of  arsenic,  or  rush  into  the  midst  of 
a  glowing  furnace,  than  if  they  verily  believed  death 
would  be  the  consequence.  And  though  in  this  it  must 
be  owned  they  act  discreetly, *yet  have  we  hence  at  the 
sarse  time  a  very  convincing  argument  of  the  absurdity 
of  those  notions  they  affect  to  entertain.  In  reality, 
can  any  thing  be  more  ridiculous,  than  to  give  into  a 
scheme  of  thinking,  which  we  find  ourselves  necessitat- 
ed to  contradict  in  almost  every  occurrence  of  life  ? 
Opinions  are  not  to  be  taken  up  out  of  caprice  and  fancy, 
but  to  serve  as  principles  of  action,  and  standing  rules 
of  behaviour.  When  they  answer  not  this  main  pur- 
pose, they  are  unavailing  and  fruitless,  and  an  obsti- 
nate adherence  to  them,  in  spite  of  the  repeated  admo- 
nitions of  experience,  justly  deserves  to  be  branded 
for  folly.  We  shall  not,  therefore,  attempt  to  multiply 
arguments  in  a  matter  so  obvious,  it  sufficiently  answer- 
ing our  present  punpose  to  have  shown,  that  doubting 
and  uncertainty  have  no  place  in  scientifical  know- 
ledger  and  that  even  in  matters  of  history,  and  the 
facts  of  nature,  and  undistinguishing  scepticism  would 
be  in  the  highest  degree  absurd. 


224  DUNCAN'S  ELEMENTS 

Sec.  XVI....  Science  applicable  to  theVencerns  of  Hu- 
man Life* 
But  here,   perhaps,    it  will  be  asked,    Why  all  this 
mighty  noise  about  science,   when,  even  according  to 
the  present  account,   it  seems  to  be  so  very  capricious 
and  arbitrary  a  thing  ?.  For  seeing  it  is  wholly  confined 
to  the  consideration  of  our  ideas,  and  we  are  at  liberty 
to  frame  and  combine  those  ideas  at  pleasure,  this    in- 
deed   opens   a   way  to  castles  in  the  air,    of  our  own 
building,   to    many    chimerical    and    fanciful  systems, 
which  men   of  warm  ^nd  lively  imaginations    love  to 
entertain  themselves  with,  but  promises  little  of  that 
knowledge  which  is  worth  a  wise   man's  regard,   and 
respects  the  great  ends  and  purposes  of  life.  Where  is 
the  advantage  of  barely  contemplating  our  ideas,    and 
tracing  their  several  habitudes  and  relations,  when  it 
is  in  truth  the  reality  of  things  that  we  are  chiefly  con- 
cerned to  know,  and  those  respects  they  bear  to  us  and 
one    another  ?   To  this  I  answer :   that  if  indeed    our 
ideas   no    way  regarded  things  themselves,  the  know- 
ledge acquired  by  their  means  would  be  of  very  little 
consequence" to  human  life.     But  since  as  we  have  al- 
ready observed,  whatever  is  true  in  idea,  is  unavoidably 
so  also  in  the  reality  of  things,  where  things  exist  an- 
swerable to  these  ideas  ;   it  is  apparent,   that  by  copy- 
ing our  ideas  with  care  from  the  real  objects  of  nature, 
and  framing  them  in  a  conforaiity  to  those  conjunctures 
and  circumstances  in  which  we  are  most  likely  to  be 
concerned,  a   way    is  laid  open   to  discoveries  of  the 
greatest  importance  to  mankind.     For  in  this  case,  our 
several  reasonings  and  conclusions,  holding  no  less  of 
the  objects  themselves,    than    of  the    ideas    by  which 
they   are  represented,  may    be  therefore  applied  with 
certainty  to  these    objects,  as  often  as  they  fail  under 
our  notice.       Thus  mathematicians,  having  formed   to 
themselves  ideas  of  cones,  cylinders,  spheres,  prisms, 
&c.  variously  compare    them   together,  examine   their 
several   properties,    and   lay  down    rules   by  which  to 
calculate  their  relative  bulk  and  dimensions.   But  now 
as   bodies  answering  in  figure  to  these  ideas  come   fre- 
quently under  our  observation,  we  have  by  this  means 


OF  LOGIC.  225 

an  opportunity  of  applying  mathematical  knowledge  to 
the  common  concerns  of  life  ;  and  by  determining 
precisely  the  quantity  of  extension  in  each  body,  can 
the  better  judge  how  far  they  will  answer  the  purposes 
we  have  in  view.  The  same  thing  happens  in  politics 
and  morality.  If  we  form  to  ourselves  ideas  of  such 
communities,  connexions, actions  and  conjuctures,as  do 
or  may  subsist  among  mankind  ;  all  our  reasonings  and 
conclusions  will  then  respect  real  life,  and  serve  as 
steadymaxims  of  behaviour  in  the  several  circumstances 
to  which  it  is  liable.  It  is  not,  therefore,  enough  that 
we  set  about  the  consideration  of  any  ideas  at  random ; 
we  must  further  take  care  that  those  ideas  truly  regard 
things  themselves  ;  for  although  knowledge  is  always 
certain,  when  derived  from  the  contemplation  of  our 
own  ideas, yet  is  it  then  only  useful  and  worthy  our  re- 
gard, when  it  respects  ideas  taken  from  the  real  objects 
of  nature,  and  strictly  related  to  the  concerns  of  hu- 
man life. 

,  Sec.  XVII....  The  method  of  science  begins  with  ascer- 
taining our  Ideas; 

Having  thus  shown  that  there  is  such  a  thing  as 
science,  fixed  and  ascertained  the  bounds  of  it,  and 
explained  its  great  use  and  importance  in  the  affairs 
of  mankind  ;  it  now  remains  that  we  lay  down  the 
rules  of  method  peculiar  to  this  branch  of  know- 
ledge, and  give  some  account  of  the  manner  in  which 
that  certainty  and  conviction  which  are  inseparable 
from  it,  may  be  most  naturally  and  effectually  pro- 
duced. Science,  as  we  have  said,  regards  wholly  the 
abstract  ideas  of  the  mind,  and  the  relations  they  have 
one  to  another.  The  great  secret,  therefore,  of  at- 
taining it  lies  in  so  managing  and  conducting  our 
thoughts,  as  that  these  several  relations  may  be  laid 
open  to  the  view  of  the  understanding,  and  become 
the  necessary  and  unavoidable  objects  of  our  percep- 
tion. In  order  to  this  we  must  make  it  our  first  care, 
distinctly  to  frame  and  settle  the  ideas  about  which 
our  enquires  are  to  be  employed.  For  as  the  relations 
subsisting  between  them  can  no  otherwise  be  discernedj 


226  DUNCAN'S  ELEMENTS 

than  by  comparing  them  one  with  another — and  as 
this  comparison  necessarily  supposes  that  the  idea, 
themselves  are  actually  in  the  mind,  and  at  that  very 
time  under  our  immediate  inspection — it  plainly  fol- 
lows, that  all  science  must  begin  with  fixing  and  ascer- 
taining those  ideas.  Now  our  ideas,  as  has  been  al- 
ready observed  in  the  first  book,  come  all  very  natu- 
rally within  the  diyision  of  simple  and  complex.  ~  Sim- 
ple ideas  are  excited  by  actual  impressions  made  upon 
the  understanding  ;  and  as  they  exist  under  one  uni- 
form appearance,  without  variety  or  composition,  arc 
in  no  danger  of  being  mistaken,  or  confounded  one 
with  another.  It  is  otherwise  in  our  complex  concep- 
tions. For  these  consisting  of  many  simple  ideas 
joined  together,  great  care  must  be  taken,  that  we  ac- 
quaint ourselves  with  the  true  number  combined,  and 
the  order  and  manner  of  their  connexion.  By  this 
means  alone  are  these  our  most  intricate  notices,  kept 
distinct  and  invariable,  insomuch  that  in  all  our  several 
views  of  them,  they  ever  have  the  same  appearance, 
and  exhibit  the  same  habitudes  and  respects.  Here, 
therefore,  properly  speaking,  the  art  of  knowledge 
begins.  For  although  we  find  it  easy  enough  tobo'und 
and  settle  our  ideas,  where  they  consist  of  but  few 
simple  perceptions  ;  yet  when  they  grow  to  be  very 
complicated,  it  often  requires  great  address  and  ma- 
nagement to  throw  them  into  such  .views  as  may  pre- 
vent that  confusion  which  is  apt  to  arise  from  tlie  joint 
consideration  of  a  multiplicity  of  different  objects. 
Hence  that  gradation  in  the  composition  of  our  ideas 
which  we  have  explained  at  large  in  the  last  chapter 
of  the  first  boek.  For  as  they  are  by  this  means  form- 
ed into  different  orders,  and  these  orders  arise  continu- 
ally one  out  of  another  ;  the  understanding,  by  taking 
them  in  a  just  succession,  gradually  mounts  to  the 
highest  conceptions,  and  can,  at  any  time,  with  incre- 
dible ease  and  expedition,  bring  all  their  parts  disinct- 
ly  into  view.  To  know,  therefore,  the  full  value  of  this 
contrivance,  we  must  attentively  consider  the  strict 
connexion  that  obtains  between  the  several  classes  of 
©ur  perceptions  when  disposed  in  such  a  series.     Eve- 


OF  LOGIC.  »r 

ry  succeeding  order  is  formed  out  of  those  combina- 
nations  that  constitute  the  rank  next  below  it.  And 
as  in  advancing  from  one  degree  to  another,  we  are 
always  to  proportion  the  number  of  notices  united,  to 
the  strength  and  capacity  ©f  the  mind  ;  it  is  apparent, 
that  by  such  a  procedure,  the  ideas  will  be  thoroughly 
ascertained  in  every  step,  and,  however  large  and 
bulky,  lie  yet  fairly  .within  our  g-asp.  This  obvious- 
ly accounts  for!'  that  wonderful  clearness  of  apprehen- 
sion, which  we  often  experience  within  ourselves,  even 
in  regard  to  the  most  complicated  conceptions.  For 
though  the  multitude  of  parts  in  many  cases  be  great, 
I  may  say  beyond  belief,  yet  as  they  have  been  all 
previously  formed  into  separate  classes,  and  the  clas- 
ses themselves  distinctly  settled  in  the  understanding  ; 
we  fii'd  it  easy,  by  such  a  series  of  steps,  to  rise  to  any 
idea,  how  complex  soever,  and,  with  a  single  glance 
of  thought,  to  embrace  it  in  its  full  extent. 

Sec.  XVIII.. ..And  Communicating  them  hy  means  of 
Definitions* 

But  it  is  not  enough  that  we  barely  form  ideas  in 
our  own  minds:  we  must  also  contrive  a  way  to  ren- 
der them  stable  and  permanent  that,  when  they  disap- 
pear upon  calling  off  our  attention,  we  may  know  how 
to  retrieve  them  .again  with  certainty.  This  is  best 
done  by  words  and  descriptions,  which  serve  not  only 
to  subject  them  to  their  own  review,but  also  to  lay  them 
open  to  the  perception  of  others.  And  indeed  as  one 
of  the  main  ends  of  reducing  knowledge  into  the 
form  of  a  science  is,  the  easy  and  advantageous  com- 
munication of  truth ;  it  ought  always  to  be  our  first 
care,  when  we  set  about  unfolding  our  discoveries,  to 
exhibit  the  several  conceptions  to  which  they  relate, 
in  a  just  and  accurate  series  of  definitions.  For  till  we 
have  distinctly  transferred  our  ideas  into  the  under- 
standings of  those  to  whom  we  address  ourselves, 
and  taught  their  connexion  with  the  appropriated 
iounds,  all  our  reasonings  will  evidently  be  without 
effect.  If  men  comprehend  not  the  true  import  of  our 
words,  and  arc  therefcre  led  by  them  to  bring  wrong 


228  DUNCAN'S  ELEMENTS 

ideas  into  comparison,  they  can  never  sure  see  connex- 
ions and  habitudes  that  really  subsit  not.  But  if,  on 
the  contrary,  the  terms  we  use,  excite  those  very  per- 
ceptions in  others,  which  they  denote  in  our  own 
minds;  then,  as  the  several  relations  pointed  out  will 
lie  fairly  open  to  view,  they  must  needs  be  discerned 
with  great  readiness  and  ease,  and  stamp  the  character 
of  certainty  upon  all  our  deductions. 

Sec.  XIX.... The  names  of  simple  Ideas  constitute  the 
original  and  elementary  terms  of  Language. 

Thus  we  see,  that  the  method  of  science  begins  with 
unfolding  our  ideas,  and  communicating  them  by 
means  of  definitions.  And  here  it  is  of  great  impor- 
tance to  observe,  that  there  must  be  in  all  languages, 
certain  original  and  elementary  names,  whence  our 
descriptions  take  their  first  rise,  and  beyond  which  wc 
cannot  trace  the  meaning  and  signification  of  sounds* 
For  since  our  very  definitions  are  made  up  of  words, 
if  we  suppose  not  such  primitive  and  fundamental 
terms,  into  which  they  all  resolve  themselves,  and 
where  they  at  last  necessarily  terminate,  it  is  evi- 
dent there  would  be  no  end  of  explaining.  Now  it  is 
peculiar  tro  our  simple  ideas,  that  they  cannot  be  origi- 
nally excited  by  words,  but  must  always  make  their 
first  entrance  into  the  understanding  by  the  actual 
operation  of  objects  upon  it.  When,  therefore,  in  a 
series  of  definitions,  we  arrive  at  the  names  of  these 
ideas, 'tis  plain  we  can  pusli  our  descriptions  no  far- 
ther, but  are  necessitated  to  suppose,  that  the  percep- 
tions themselves  have  already  found  admission  into  the 
mind.  If  they  have  not,  definitions  avail  nothing  ;  nor 
can  they  any  other  way  be  impressed  upon  us,  than 
by  betaking  ourselves  to  the  several  objects  in  which 
the  power  of  producing  them  resides.  Hence  it  ap- 
pears, that  the  primary  articles  of  speech,  into  which 
the  whole  of  language  may  be  ultimately  resolved^ 
are  no  other  than  the  names  of  simple  ideas.  These, 
we  see,  admit  not  definitions.  It  is  by  experience  and 
observation,  that  we  grow  acquainted  with  their  mean- 
ing, and  furnish  ourselves  with  the  perceptions  thejr 


OF  LOGIC.  229 

jerve  to  denote.  For  finding  that  those  in  whose  soci- 
ety we  live,  make  use  of  certain  articulate  sounds,   to 
mark  the   various  impressions  of  objects,  we    too  an- 
nex these    sounds  to    the  same    impressions,  and  thus 
Come  to  understand  the  import  of  their  words.     This 
way  of  knowledge   takes   place,  in   regard   to   all  our 
simple  ideas  ;  but  in  many  of  those  that  are  complex,  as 
they  are  the  mere  creatures  of  the  understanding,  and 
exist  no  where   out  of  the  mind,  there  are,  of  course, 
no  real  objects  without  Us,  whence  they  may  be  origi- 
nally obtained.     If,  therefore,  they  could  not  be  com- 
municated by  descriptions,  we   should  be   left  wholly 
without  the  means  of  transferring  them  into  the  minds 
of  others.     But  happily  it  so  falls  out,    that  all  cor» 
"plex  conceptions  whatsoever  may  be  distinctly  exhibit- 
ed in  definitions.     For  as  they  are  no  more  than  differ- 
ent combinations  of  simple  ideas,  if  these  simple  ideas 
have  already    got   admission   into  the   understanding, 
and  the  names  serving  to  express  them  are  known  ;  it 
will  be  easy,  by  describing  the  order,  number,  and  pe- 
culiar connexion   of  the  notices  combined,    to  raise  in 
the  mind  of  another  the  complex  notion  resulting  from 
them. 

Sec.  XX.. ..A  Knowledge  of  these  previously  supposed 
in  handling  any  Subject  scientifically* 

Since  then  it  is  by  simple  ideas  and  their  names, 
that  we  unfold  all  the  other  conceptions  of  the  mind  ; 
it  manifestly  follows,  that  in  handling  any  subject, 
scientifically,  we  must  always  suppose  those  to  whom 
we  address  ourselves,  previously  furnished  by  experi- 
ence with  these  first  principles  and  elements  of  know- 
ledge. Nor  is  this  by  any  means  an  unreasonable pos* 
tulatum :  because  the  simple  ideas  that  relate  to  the 
sciences,  being  few  in  number,  and  coming  very  often 
in  our  way,  it  is  hardly  possible  we  should  be  unac- 
quainted with  them,  or  not  have  frequently  heaid  their 
names  in  converse  with  others.  What  principally  de- 
mands our  care  is,  to  apply  those  names  aright  and  ac- 
cording to  the  strict  use  and  propriety  of  the  language 
in  which  wc  write.     'Tis  seldom  allowable  to  change 

u 


230  DUNCAN'S  ELEMENTS 

the  signification  of  words,  especially  those  by  which 
we  denote  simple  ideas.  If,  however,  such  a  liberty 
should  at  any  time  be  found  necessary,  We  may  still 
make  ourselves  understood,  by  mentioning  the  idea  un- 
der its  common  name,  and  signifying  its  connexion 
with  the  newly  appropriated  sound.  Indeed  it  some- 
times happens,  that  new  and  unusual  ideas  of  this  kind 
are  to  be  taken  under  consideration,  which  we  must 
therefore  express  by  terms  of  our  own  invention.  In 
this  case,  as  the  ideas  themselves  cannot  be  laid  open 
by  definitions,  we  refer  to  the  several  objects  whence 
they  may  be  obtained  ;  which  though  it  excites  not 
the  perceptions  immediately,  yet  sufficiently  answer* 
our  purpose,  by  putting  men  in  a  way  of  being  furnish- 
ed with  them  at  pleasure. 

Sec.  XXL...  The  order  and  connexion  of  our  Definitions* 

This  foundation  being  laid,  the  communication  of 
our  complex  conceptions  by  definitions  becomes  both 
easy  and  certain.  For  since  the  ideas  themselves  are 
formed  into  different  orders,  and  these  orders  arise  con- 
tinually one  out  of  another  ;  nothing  more  is  required 
on  our  part,  than  to  observe  a  like  method  and  grada- 
tion in  our  descriptions.  As,  therefore,  the  first  order 
of  our  compound  notions  is  formed  immediately  from 
simple  ideas  ;  so  the  terms  appropriated  to  this  order 
must  be  defined  by  the  names  of  these  ideas.  And  as 
the  second  and  all  the  .succeeding  orders  arise  continu- 
ally out  of  those  combinations  that  constitute  the  clas- 
ses next  below  them,  so  the  definitions  corresponding 
to  these  different  orders  gradually  take  in  the  terms  by 
which  the  several  inferior  divisions  are  regularly  and 
successively  expressed.  In  such  a  series  of  descriptions, 
it  is  evident,  at  first  sight,  that  nothing  can  be  ob- 
scure and  unintelligible.  For  as  it  begins  with  the 
names  of  simple  ideas,  whose  meaning  is  supposed  to 
be  known — and  as  in  every  order  of  definitions,  such 
terms  only  occur,  as  have  been  previously  explained  in 
the  preceeding  distributions-— by  advancing  regularly 
from  one  to  another,  we  gradually  furnish  ourselves 
with  whatever  is  necessary  towards  a  distinct  concep- 


OF  LOGIC  231 

tion  of  all  that  is  laid  before  us.  Nor  is  it  a  small 
advantage  attending  this  disposition,  that  the  several 
ideas  described  are  hereby  excited  in  the  understand- 
ing, in  the  very  order  and  manner  in  which  they  are 
framed  by  a  mind  advancing  uniformly  from  simple  to 
the  most  complicated  notions.  Hence  we  see  distinct- 
ly the  various  dependence  of  things,  and  being  put  in* 
to  that  very  train  of  thinking  which  leads  directly  to 
science  and  certainty,  are  drawn  insensibly  to  interest 
ourselves  in  the  pursuit  ;  insomuch,  that  while  in  fact 
we  do  no  more  than  follow  a  guide  and  conductor,  we 
fan  yet  hardly  forbear  fancying  ourselves  engaged  in 
the  actual  exercise  of  deducing  one  part  of  knowledge 
from  another. 

Sec.  XXII.. ..0/  the  immediate  and  intuitive  Relations 

betioeen  our  Ideas. 

When  we  have  thus  fixed  and  ascertained  our  ideas, 
and  distinctly  exhibited  them  in  definitions,  we  then 
enter  upon  the  important  task  of  tracing  their  several 
habitudes  and  relations.  In  order  to  this,  we  set  about 
comparing  them  among  themselves,  and  viewing  them 
in  all  the  variety  of  lights,  by  which  we  can  hope  to 
arrive  at  a  discovery  of  their  mutual  agreement  or 
disagreement.  And  here  it  happens,  that  some  rela- 
tions forwardly  oiler  themselves  to  the  notice  of  the 
understanding,  and  become  the  necessary  objects  of 
perception,  upon  the  very  first" application  of  our  ideas 
one  to  another.  Those  are,  therefore,  immediately- 
owned,  and  constitute  our  primary  and  intuitive  judg- 
ments, being  attended  with  the  highest  degree  of  evi- 
dence, and  producing  absolute  certainty  in  the  mind. 
B  iu  ill  many  cases,  the  connexion  or  repugnance  be- 
tween our  ideas,  even  when  true  and  real,  comes  not 
yet  within  our  immediate  view,  but  requires  search 
and  examination  to  discover  it.  On  this  occasion,^we 
have  recourse  to  intermediate  notices,  and  if  by  means 
of  them  we  can  muster  up  a  train  of  evident  and  known 
truths,  which,  disposed  in  a  regular  series  of  argumen- 
tation, lead  at  last  to  a  conclusion  expressing  the  rela- 
tions we  are  in  cuest  of,  the  proof  theiice   arising  is 


232  DUNCAN'S  ELE  MENTS 

called  demonstration.     Now  as  the  conviction  attending 
demonstration,  is  no  less  necessary  and  unavoidable  than 
that  which  proceeds  from  intuition;    it  evidently  fol- 
lows,   that    whether  the  delations    between    our   ideas 
are   immediately  discerned  by  the  mind,    or  whether 
they  are  traced  by  means  of  intervening  perceptions,  in 
either  case  we  arrive   at  science  and  certainty.     This, 
however,  is  particularly  to  be  observed,  that  the  more 
remote  and  distant  respects,  being  deduced  from  such 
as  are  obvious  and  self-evident,  the  propositions  expres- 
sing these  last  demand  our  first  notice,  and  ought  to  be 
previously  established,  before  we  enter  upon  higher  in- 
vestigations.       When,    therefore,    in   the    method  of 
science,    we  have  finished  the  business  ot  definitions  ; 
it  must  be  our  next  care,  distinctly  to  unfold  in  propo- 
sitions, those  immediate  and  intuitive  relations,  which 
are  necessarily  seen  and  owned  by  the  mind,  upon  the 
very  first  comparing  of  our  ideas  one  with  another.  These 
propositions  have  obtained  the  name  of  Jirst  principles, 
because,   occurring  first  in   the   order   of   knowledge, 
and  being  manifest  of  themselves,    they  suppose    not 
any  prior  truths  in  the  mind,  whence  they  may  be  evi- 
denced and  explained.   %    It  is  not  needful   to  enlarge 
here  upon  the  necessity  of  circumspection  and  care,  in 
setrling  these   primitive  and  fundamental  perceptions. 
For  since  the  whole  superstructure  of  our  knowledge 
rests  ultimately  upon  them,  it  is  evident  at  first  sight, 
that  a  mistake  in  this-case  must  at  once  overturn   and 
annihilate^  all-  our  future  reasonings.      But  having  al- 
ready explained  the  nature  of  these  propositions  in  th« 
second  book,  unfolded  the  notion  of  self-evidence,  and 
taught  the  manner  of  distinguishing  between  the  truths 
of  this  class,    and"  those   that  are  demonstrable;    we 
fell  all,  for  the  present,  wave   any  farther  consideration 
of  this  subject,    referring  the  reader  to   what  is  there 
advanced,  if  he  desires  fuller  information. 

Sec.   XXIU....Of  the  application  of  Self  evident  truths 
in  demonstrating  such  as  are  remote  and  distant. . 

The  first  and  more  immediate  relations  of  our  ideas 
being  thus  pointed  out,  'our  next  business  is,  to  investi- 


OF  LOGIC.  233 

gate  such  as  are  remote  and  distant.  And  here  it  is 
that  we  have  occasion  for  intermediate  notices,  and  a 
skilful  application  of  intuitive  truths.  But  though 
self-evident  propositions  he  the  ultimate  foundation  of 
our  reasoning,  we  are  not,  on  that  account,  to  imagine, 
that  the  art  of  improving  knowledge  lies  in  assembling, 
at  random-,  a  large  and  comprehensive  stock  of  these. 
Even  general  principles,  considered  by  themselves,  avail 
but  little  towards  the  investigation  of  truth.  They  are, 
indeed,  useful  as  media  of  certainty,  by  preserving  the 
evidence  of  our  reasonings  distinct,  which  never  fail  to 
convince,  if,  being  pursued  to  their  source,  they  are 
found  to  resolve  themselves  into,  and  ultimately  termi- 
nate in  these  principles.  But  when  we  set  about  the 
increase  and  enlargement  of  science,  far  other  helps 
are  required.  For  here  the  whole  secret  consists,  in 
devising  and  singling  out  such  intermediate  ideas,  as, 
being  compared  with  those  others  whose  relations  we 
enquire  after,  may  furnish  out  a  train  of  obvious  and 
known  truths,  serving  distinctly  to  investigate  the  said 
relations.  Euclid,  In  the  first  book  of  the  elements, 
hasHlemonstrated,  that  the  three  inward  angles  of  a 
triangle  taken  together,  are  equal  to  two  right  angles. 
The  reasoning,  by  which  he  establishes  that  proposition, 
resolves  itself  into  this  general  principle  :  things  equal 
to  one  and  the  same  thing,  are  equal  to  one  another. 
Will  any  one,  however,  pretend  to  say,  that  a  bate 
consideration  of  the  principle  itself  led  him  t©  that  dis- 
covery .?  the  merest  novice  in  mathematics  would,  up- 
on this  supposition,  be  equally  qualified  for  the  business 
of  invention,  with  one  that  had  made  the  greatest  pro- 
gress ;  inasmuch  as  these  general  principles  of  the 
science  are  commonly  alike  known  to  both.  But  the 
truth  of  it  is,  Euclid,  having  found  out  angles,  to 
which  the  three  angles  of  a  triangle,  and  two  right 
angles,  being  compared,  were  found  severally  equal  ; 
thereby  ascertained  the  proposition  in  question,  by- 
showing  it  to  terminate  in  the  above  axiom,  though 
perhaps  the  axiom  itself  was  never  once  thought  of, 
during  the  whole  course  of  the  investigation. 

U  2 


234  DUNCAN'S  ELEMENTS 

Sec.  XXIV....  Reasoning,  though  resolvable  into  gene- 
ral truths,  rests  immediately  upon  particular  self- 
evident  propositions. 

And  here  it  may  not  be  improper  to  observe,  that 
though  it  be  usual  in  reasoning,  when  we  arrive  at  any 
particular  self-evident  proposition,  to  refer  to  the  ger- 
neral  axiom  under  which  it  is  comprehended  :  yet  is 
not  this  done  out  of  absolute  necessity,  01  ft  r  the  sake 
of  any  additional  confirmation.  All  intuitive  truths, 
whether  general  or  particular,  standing  upon  the  same 
foundation  of  immediate  perception,  are  necessarily 
embraced  for  their  own  sake,  and  require  no  mutual 
illustration  one  from  another.  When,  therefore,  ve 
have  found,  that  the  three  angles  of  a  triangle,  and 
two  right  angles,  are  severally  equal  to  the  angles  form- 
ed by  one  right  line  standing  upon  another,  we  thence 
immediately  discern  their  equality  between  themselves, 
independent  of  the  general  axiom  into  which  this 
truth  may  be  resolved.  Nor  do  we  in  reality  refer  to 
that  axiom,  by  way  of  evidence  and  proof;  but  merely 
to  show  the  coincidence  of  the  example  under  notice, 
with  a  previously-established  general  principle.  The 
same  thing  happens  in  all  other  demonstrations  whatso- 
ever, which,  terminating  thus  in  particular  self-evi- 
dent truths,  are  therefore  of  themselves  sufficient  to 
.certainty,  and  acquire  not  any  new  force  by  being  ul- 
timately referred  to  general  maxims.  This  I  mention 
here,  to  obviate  a  common  prejudice,  whence  many  are 
led  to  imagine,  that  particular  intuitive  propositions 
derive  their  evidence  from  those  that  are  general,  as 
being  necessarily  included  in  them.  But  since  they 
both  stand  upon  the  same  foundation  of  certainty, 
and  are  admitted  in  consequence  of  immediate  percep- 
tion, they  have  therefore  an  equal  claim  to  self-evi- 
dence, and  cannot  be  made  plainer  by  any  mutual  ap- 
peal. 

Sec.    XXV.... Particular   Self-evident  propositions  so 
called  herey  in  opposition  to  general  principles. 

As,  however,  it  is  usual  in  the  method  of  science  to 


OF  LOGIC.  23* 

lay  down  certain  general  principles  by  way  of  founda- 
tion for  our  future  reasonings;  some  will  perhaps,  ab- 
ject, that  this  seems  to  be  a  needless  precaution,  since 
d  -monstrations  may  subsist  without  them,  and  commonly 
terminate  in  particular  self-evident  truths,  peculiarly 
connected  with  the  subject  under  consideration.  In 
oider,  therefore,  to  give  a  distinct  idea,  of  the  true  de- 
:  of  this  previous  step,  we  shall  begin  with  observ- 
ing, that  by  the  particular  propositions  in  which  de- 
monstrations terminate,  must  not  be  understood  such  as 
are  so,  according  to  the  strict  definition  of  the  word, 
or  in  opposition  to  universal  ;  but  only  confined  and 
limited  truths,  when  compared  with  others  that  are 
more  general.  Thus  the  proposition,  circles^  equal  to 
one  and  the  same  circle,  are  equal  between  themselves, 
is,  in  strictness  and  propriety  of  speech,  universal,  be- 
cause the  subject  is  taken  in  its  full  extent,  and  the 
pred,   i  es  to  all  the  individuals  comprehended  un- 

der it.  We  here,  notwithstanding,  consider  it  as  on- 
ly a  particular  truth;  because  it  is  of  a  very  limited 
nature,  when  compared  with  the  general  axiom  men- 
tioned above  ;  things  equal  to  one  and  the  same  things 
are  equal  to  one  another.  For  this  not  only  extends  to 
all  the  various  species  of  figures,  but  takes  in  every  ob- 
ject without  exception,  that  comes  under  the  denomi- 
nation of  quantity. 

Sec.   XXV 'I..,. General  Principles  serve,  first,  to  Con- 
tract the  bottom  of  our  Reasoning. 

This  point  settled,  it  will  easily  appear,  that  the  me- 
thod of  premising  general  principles  in  the  sciences 
answers  these  two  great  and  valuable  purposes.  First, 
to  cbntract  the  bottom  of  our  reasoning,  and  bring  it 
within  such  bounds  as  are  sufficiently  accommodated 
to  the  capacity  of  the  mind.  For  demonstrations  be- 
ing carried  on  by  means  of  intermediate  ideas,  which 
must  always  have  some  peculiar  connexion  with  the 
matter  in  hand,  the  particular  self-evident  propositions 
in  which  they  terminate,  are  almost  as  various  as  the 
subjects  to  which  they  relate.  Thus  in  investigating 
the  equality  of  different  objects,  whether  angles,  trian- 


236  DUNCAN'S  ELEMENTS 

gles,  circles,  squares,  Sec.  the  intuitive  truths,  oa 
which  the  proofs  rest,  always  regard  the  particular  spe- 
cies, and  may  be  therefore  multiplied,  in  ihjinitum,  as 
"well  as  the  species  themselves.  But  now  it  is  remark- 
-  able,  that  all  these  several  truths,  numerous  as  they 
may  appear,  are  yet  reducible  to  this  one  general  prin- 
ciple already  mentioned  ;  things  equal  to  one  and  the 
same  thing  are  equal  to  one  another.  The  same  obser- 
vation will  be  found  to  hold  in  other  parts  of  human 
knowledge  ;  insomuch  that  though  the  particular 
truths,  on  which  we  bottom  our  reasonings,  are  really 
innumerable  ;  yet  may  they  be  all,  without  exception, 
resolved  into  a  very  few  general  maxims,  and  thereby 
brought  readily  within  the  compass  of  the  understand* 
ing.  When,  therefore,  we  begin  with  premising  these 
general  truths,  and  as  we  advance  in  science,  take  care 
universally  to  resolve  our  demonstrations  into  them  ; 
this  must  needs  add  a  wonderful  clearness  and  perspi- 
cuity to  our  reasonings,  and  by  establishing  them  upon  a 
foundation  previously  admitted,  and  of  whose  strength 
and  firmness  we  are  abundantly  satisfied,  give  them  that 
irresistable  force  and  influence,  which  serves  to  produce 
absolute  certainty.  Nor  can  we  possibly  imagine  any 
thing  more  elegant  and  beautiful,  than  thus  to  behold 
knowledge  rising  from  a  firm  and  fathomable  root, 
bearing  its  head  aloft,  and  spreading  forth  into  innu- 
merable branches  of  science  ;  which,  though  various- 
ly implicated  and  entangled,  and  stretching  to  a  vast 
extent,  yet  by  their  union  in  one  common  stock,  derive 
thence  so  sure  and  stable  a  support,  that  all  the  as- 
saults of  cavil  and  scepticism  are  not  able  to  destroy 
or  loosen  their  connexion. 

Sec.   XXV 'II... .Secondly,  to  ascertain  the  Justness  of 
it  with  more  Ease,  and  less  Hazard  of  Miscarriage. 

But,  secondly,  another  purpose  served  by  general 
principles  is,  that  they  enable  us  with  less  fatigue  and 
labour  and  less  hazard  of  miscarriage,  to  satisfy  our- 
selves as  to  the  justness  of  those  reasonings  by  which, 
science  is  established.  For  since  demonstrations,  when 
pursued  to  their  source,  terminate  always  in  particular 


OF  LOGIC.  23? 

intuitive  truths,  -which  are  therefore  the  ultimate  foun- 
dation of  certainty  ;  it  greatly  improves  u?,  to  beware, 
that  we  receive  not  any  propositions  under  this  name, 
until  we  have  distinctly  settled  them  in  our  own  minds, 
and  attained  a  full  and  clear  perception  of  that  self-evi- 
dence, on  account  of  which  they  are  admitted  without 
proof.  But  now  these  propositions  being  many  in  num- 
ber, and  differing  according  to  the  nature  of  the  subject 
about  which  our  researches  are  employed  ;  it  mustgreat- 
'ly  perplex  and  retard  our  reasonings,  were  we  to  check 
ourselves  every  time  they  occur,  in  order  to  examine 
them  by  the  rules  of  first  principles.  Nor  is  it  a  matter 
of  slight  consideration,  that  in  the  heat  and  hurry  of 
demonstrating,  while  the  mind  is  advancing  eagerly 
from  one  discovery  to  another,  we  should  be  often 
tempted«to  pass  them  over  hastily,  and  without  that 
attention  their  importance  requires  ;  which  must  ex- 
pose us  to  many  errors  and  mistakes.  These  inconve- 
niences are  effectually  prevented  by  the  method  of  pre- 
mising general  truths  :  because  upon  referring  particu- 
lar propositions  to  them,  as  the  connexion  is  obvious  at 
first  sight,  and  cannot  possibly  escape  our  notice,  the 
evidence  is  discerned  to  be  the  very  same  with  that  of 
the  principles  to  which  they  belong.  And  thus  by  a 
bare  reference,  without  the  trouble  of  particular  ex- 
aminations, the  grounds  of  reasoning  are  ascertained, 
and  our  demonstrations  found  ultimately  to  rest  on 
maxims  previously  established. 

Sec*  XXVI II.. ..Of  the  manner  of  linking  propositions 
togtthtr,  in  order  to  the  for  miyig  of  legitimate  demon- 
strations.. 

Having  explained  the  use  of  general  principles, 
shown  them  to  be  the  great  media  of  certainty,  and 
found,  that  in  order  to  enlarge  the  bounds  of  science, 
we  must  have  recourse  to  intermediate  ideas,  as  by 
means  of  them  we  are  furnished  with  the  several  pre- 
vious truths,  of  which  reasoning  consists  ;  it  now  re- 
mains, that  we  enquire  in  what  manner  these  truth* 
are  to  be  disposed  and  linked  together,  towards  the 
forming  of  just  and  legitimate  demonstrations.  We  have 


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